C2 sequences and series binomial expansion answers

 

a. 1 3 marks. So the term containing x6 is. Let’s look for a pattern in the Binomial Theorem. (a) Find the first 3 terms, in ascending powers of x, of the binomial expansion of (2 + kx)7. Find the first 4 terms of the binomial expansion, in ascending powers of x, of :1+𝑥 4 ;8 giving each term in its simplest form. (2) Given that the third term of this series is 540x 2 , (b) show that k = 6, (2) (c) find the coefficient of x 3. Find the first 3 terms, in ascending powers of x, of the binomial expansion of. 1 anything that cancels to 2 Simplified —Xx2 — x Attempt to substitute 0. \displaystyle {\left ( {a}+ {b}\right)}^ {5} (a +b)5. Questions and answers with explanations on binomial theorems Sequences and series - Binomial series PhysicsAndMathsTutor. E: Sequences, Series, and the Binomial Theorem (Exercises) is shared under a CC BY-NC-SA 3. 13 a Expand (3 – 3 x)12 as a binomial series in ascending powers of x up to and including the term in x3, giving each coefficient as an integer. The first three terms in the expansion of (1 + ax)b, in ascending powers of x, for |𝑎𝑎| < 1𝑥𝑥, are 1 – 6x+ 24x2. Example 5. 034 642 080 = 527 205. = 1 + 12x+ 48x2+ 64x3= 1 − 6y+ 12y2− 8y3. Sequences and series - Binomial series PhysicsAndMathsTutor. x)12 as a binomial series in ascending powers of x up to and including the term in x3, giving each coefficient as an integer. Define geometric sequence as a sequence in which each term after the first is found by multiplying the preceding term by a constant ratio. Feb 14, 2022 · Exercise 12. [3] (ii) Given also that the coefficient of . Key Skills. 1st class MSci Astrophysics. Download these Free Sequences and Series MCQ Quiz Pdf and prepare for your upcoming exams Like Banking, SSC, Railway, UPSC, State PSC. The binomial coefficients are the integers calculated using the formula: (n k) = n! k!(n − k)!. In an arithmetic progression the sum of the first ten terms is 400 and the sum of the next ten terms is 1000. (4) (b) Use this expansion with your values of p and q together with an appropriate value of x C2 Sequences & Series: Binomial Expansion www. b n. 97 10. Dec 27, 2014 · C2 Sequences & Series: Binomial Expansion 1. 3√8−2x 8 − 2 x 3 Solution. 43 JEE Main Mathematics Online (2019-2012) & Offline (2018-2002) Chapter-wise + Topic-wise Solved Papers 3rd Edition 2011-03-08 Brooks/Cole. Solution: Let us take a = 3 and b = 2x in the binomial expansion of (a + b) 10. Pearson Education accepts no responsibility whatsoever for the accuracy or method of working in the answers given. Show Step-by-step Solutions Binomial Expansion 1a. Therefore, the general term is expressed in terms of the previous two as follows: F n = F n − 2 + F n − 1. 5. (a) Find the first 4 terms, in ascending powers of x, of the binomial… C2-Sequences-Series-C-Simple-Binomial-Expansion-Answers. C2 Sequences and Series. Jan 3, 2023 · A sequence is simply a list of numbers in a particular order. where b is a non-zero constant. Oct 6, 2021 · This page titled 9. 025) 8 giving your answer to 4 decimal places. and for the cube of a binomial, we obtain after expanding. in the expansion is 128, find the values of . and . ak = 2. x)2+ 4(1 2. SEND. (4) Given that the coefficient of . 2 = (1 − 2 )1 2. b the value of the coefficient of x3 in the expansion. --> 512 + 11520x + 115200x² --> 512 + 11520(0. 4 in ascending powers of x up to and including the term in x3 is. [4] C2 Sequences and Series. The Binomial Expansion, is a theorem which allows us to expand (a + b)^n, where n is an integer. Nov 16, 2022 · This is useful for expanding (a+b)n ( a + b) n for large n n when straight forward multiplication wouldn’t be easy to do. [2] (b) x3 17. Give each term in its simplest form. Symbolise this as a, ar, ar²,…. Jan 2009 qu. For example. Sequences and Series Key Skills Section (for selecting more than one) Jan 24, 2012 · The Sequence and Series chapter in c2, is quite big, so I will divide it into 3 / 4 posts. (4) (c) Hence find the coefficient of x in the expansion of . (a) Find the first 4 terms, in ascending powers of x, of the binomial… AS and A level Mathematics Practice Paper – Binomial expansion – Mark scheme 5 Source paper Question number New spec references Question description New AOs 1 C2 2012 1 4. To calculate the 50th partial sum of this sequence we need the 1st and the 50th terms: a1 = 4 a50 = 5 − 1 = 249. + 9x + px2 + qx3, 12x < 1. (4) (b) Use this expansion with your values of p and q together with an appropriate value of x to obtain an estimate of (1. (a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of (1 + ax)7, where a is a constant. It should also be obvious to you that (a + b)¹ = a + b . For instance, 2,4,6,8 are the first four terms in the sequence of even positive integers. b Use your series expansion with a suitable value of x to obtain an estimate for 2. 17. (4) (Total 9 marks) (a) (i) Using the binomial expansion, or o therwise, express (2 + y)3 in the form Geometric Sequences and Series. b. Next use the formula to determine the 50th partial sum of the given arithmetic sequence. a Find the first 4 terms, in ascending powers of x, of the binomial expansion&#8230; In the binomial expansion of (1 + x)40, the coefficients of x4 and x5 are p and q respectively. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team. the Binomial Theorem 8. Questions and model answers on 4. As a farmer bales a Transcript. The exponents on b increase by one on each term going left to right. 3. 1b 3 C2 2015 1 4. Pascal’s Triangle. 4: Binomial Theorem The binomial theorem provides a method of expanding binomials raised to powers without University of Glasgow - MSc Astronomy and Physics. But with the Binomial theorem, the process is relatively fast! Created by Sal Khan. 𝑎𝑎𝑎𝑎+ 𝑏𝑏). All C2 Revsion Notes. You can find Edexcel International A-level P2 (WMA12), C12 (WMA01), and Edexcel A-level old spec C2 (6664), past papers, mark schemes and model answers below: expand. C2-Sequences-Series-C-Simple-Binomial-Expansion-Answers. This sequence is known as Pascal's triangle. g. Use Pascal’s triangle to quickly determine the binomial coefficients. 2: Arithmetic Sequences and Series; 9. Then, x6 will appear in the term containing (2x) 6 and nowhere else. Follows correct answer with 27 90x+120x2 can iswhere (sp marks for correct answer Misreads ascending and gives —32x5 + 240x4 — 720x3 is marked as BIBOMIAO special case and must be completely correct (If any slips could get BOBOMIAO) Ignores 3 and expands (1 ± 2x)5 is 0/4 243, -810x, 1080x2 is full marks but243, -810, 1080 is GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Hint: use Pascal’s triangle and binomial expansion: (a) x4 + 4x3 + 6x2 + 4x+ 1. Find the series expansion of f(x) in ascending powers of xup to and including the term in x3and state the set of value of x for which it is valid. (4) (b) Use this expansion with your values of p and q together with an appropriate value of x = 4. 1b 2 C2 2017 1 4. (4) Given that the coefficient of x2 in this expansion is 525, (b) find the possible values of a. (a) Find the first 4 terms, in ascending powers of x, of the binomial… In the binomial expansion of (k + ax)4 the coefficient of x2 is 24. a n. 03 (2dp) Solomon Edexcel Worksheets and answers for the C2 module. c) Use the answer of part (b) to estimate, correct to 2 significant figures, the C2 Sequences & Series: Binomial Expansion PhysicsAndMathsTutor. Rewriting so the power is visible. 99812 ≈ 531 441 − 4251. x , } expansion With candidate' s followed through ( ** x) Award SC Ml if you see Either 2 {1. The binomial theorem provides a method for expanding binomials raised to powers without directly multiplying each factor: (x + y)n = n ∑ k = 0(n k)xn − kyk. co. Questions are taken from the pre 2010 exam papers. In the following exercises, find the coefficient of the indicated term in the expansion of the binomial. n + 1. In the 3 rd row, flank the ends of the rows with 1’s, and add [latex]1+1 [/latex] to find the middle number, 2. The Binomial Series. Answer. Answer: 2, −4, 8, −16, 32. When we take the sum of the terms in a sequence, we get a series. Find the values of the constants a, b and c. are both positive, show that . £55 / hour. 1b 17. Sep 19, 2022 · Help Center Detailed answers to any questions you might have Using the binomial expansion for $ sequences-and-series; Feb 14, 2022 · The real beauty of the Binomial Theorem is that it gives a formula for any particular term of the expansion without having to compute the whole sum. 23 Use the Binomial Theorem to Expand a Binomial. k. 3 2 (2) (b) Find the first term of the sequence. (a) Find the first 4 terms of the binomial expansion, in ascending powers of x, of (1 + x/4)8 giving each term in its simplest form. In the [latex]n\text {th} [/latex] row, flank the ends of the row with 1’s. aectutors. (9−x)4 ( 9 − x) 4 Solution. 𝑦𝑦 We can either use the binomial formula or Pascal’s triangle to expand expressions of the form (𝑎𝑎+ 𝑏𝑏)𝑛𝑛. The binomial expansion Exercise A, Question 6 © Pearson Education Ltd 2008 Question: The coefficient of x2 in the expansion of ( 2 + ax ) 3 is 54. (2) (Total 6 marks) 2. 1 Into a candidate's binomial expansion. where k is a constant. 03 (2dp) an = a1 + (n − 1) d = 4 + (n − 1) ⋅ 5 = 4 + 5n − 5 = 5n − 1. Thus, if we denote the terms of a binomial by a and b, the square of a binomial gives after expanding it. All C1 Revsion Notes. ) If we wish to expand an expression of the form , then we can use the above formula by replacing every with . This section looks at Binomial Theorem and Pascals Triangle. 1 Binomial Expansion for the Edexcel A Level Maths: Pure a) Determine, in ascending powers of x, the first three terms in the binomial expansion of ( )2 3− x 10. (a) Find the first 4 terms, in ascending powers of . 792 Binomial Expansion of (ax±b) n, Where n is a Positive Integer. London Science College © 2024 Geometric Progressions, where we multiply by a fixed number to get each new term of the progression. x, of the binomial expansion 5. 7 Feb 19, 2024 · The number of terms is n + 1. com Edexcel Internal Review 1 . x. (12) 6. 3a. Familiarise with the formulae of a geometric sequence: nth term = ar^ (n - 1) and sum of first n terms = a (1 - r^n) / (1 - r) when. A sequence (or series) is divergent if and only if it is not convergent. Find the value of p and the value of q. The first term is an. 001) + 115200(0. 3 Geometric Sequences and Series 418 8. in ascending powers of . 025)8, giving your answer to 4 The third term of a geometric sequence is 324 and the sixth term is 96 (a) Show that the common ratio of the sequence is . 1 Binomial Expansion for the OCR A Level Maths: Pure syllabus D1-1 9 Binomial Expansion: EXTENSION Extending Binomial Expansion D1- 20 Binomial Expansion: Writing (a + bx)^n in the form p(1 + qx)^n D1- 21 Binomial Expansion: Find the first four terms of (1 + x)^(-1) All A level questions arranged by topic. Solomon Press. Term in x2 is 3 × 21 × (x a ) 2 = 6a2x2 C2 SEQUENCES AND SERIES Answers - Worksheet D page 4 Solomon Press 13 a = 312 + 12(311)(− 3 x) + 12 11 2 × (310)(− 3 x)2 + 12 11 10 32 ×× × (39)(− 3 x)3 + … = 531 441 − 708 588x + 433 026x2 − 160 380x3 + … b let 3 x = 0. e= 1 + 4(1 2. [4] (iii) Hence find the coefficient of . Experienced Mathematics Tutor for GCSE, A levels and IB. For instance, for "small" x, 1 + nx is a "reasonable" approximation for (1 + x)n. Consider a geometric sequence with kth term a k = ark such that: a 1 = 1; X1 k=0 ark = 9 2: (a)Either a = 3 and r = 1 3, or a = 3 2 and r = 2 3. (a) Find the value of p and the value of q. For example, 2+4+6+8+ is a series. 1b 4 C2 June 2014R 1 4. 2. (2) (Total 6 marks) For the binomial expansion, in descending powers of x, of; 12 3 2. The sum of the exponents on any term is n. Let’s take a quick look at an example. The binomial expansion of (1 + 12 x ) 3. (a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3. 001)² --> 523. 005⁹ --> ∴ x = 0. and the last term is bn. Binomial Expansion 1a. 5 Find the coefficient of x6 in the expansion of (3 + 2x) 10. Model Answers. 0003125 1. Figure 12. P2 | C12 | C2. 528 + 15. p5q4 term of (3p + q)9. 006 2. 2 Arithmetic Sequences and Series 409 8. x5 term of (x − 4)6. x . 14 a Expand (1 – x)5 as a binomial series in ascending powers of x. [5] 11. Find an expression for b in terms of a. com Edexcel Internal Review 1 1. 97468099. (4) Given that the coefficient of x2 is 6 times the coefficient of x, (b) find the value of k. 1 Binomial expansion 1. Example 1 Use the Binomial Theorem to expand (2x−3)4 ( 2 x − 3) 4. b) Use the first three terms in the binomial expansion of ( )2 3− x 10, with a suitable value for x, to find an approximation for 1. Nov 16, 2022 · For problems 1 & 2 use the Binomial Theorem to expand the given function. com. where P(r / n) is the probability to observe the event r / n of r successes out of n trials. 1 9746810 2 0. P(r / n) = ∑ni = 0Cniqn − ipiδir = Cnrqn − rpr. 1 Infinite Sequences 401 8. x6 term of (x + 2)8. < 1 35 terms of the series. k . Therefore, the general term is an = 5n − 1. (5) 4. This topic is included in Paper 1 for AS-level Edexcel Maths and Papers 1 & 2 for A-level Edexcel Maths. And the sum $1-1+1-1+\cdots$ is not convergent, because the sequence of its partial sums (which is $1,0,1,0,1,0\cdots$) is not convergent (because it does not have a limit). The New 2017 A level page. Expand the following expressions. 1. Binomial Expansion Series, Sequences, and Binomial Expansion Test Calendar Subject to Change! HW 1: HW 7: Answer all questions in #1 – 6: 1. (2) (c) Find the sum of the first 15 terms of the sequence. (4+3x)5 ( 4 + 3 x) 5 Solution. Jan 2, 2012 · C2 Edexcel Core Mathematics January 2012 Question 3 Binomial Expansion 3. Notice, that in each case the exponent on the \(b\) is one less than the number of the term. The Binomial theorem tells us how to expand expressions of the form (a+b)ⁿ, for example, (x+y)⁷. f(x) =3+5𝑥𝑥 (1+3𝑥𝑥)(1+𝑥𝑥)2. (3) (d) Find the sum to infinity of the sequence. Find the possible values of the constant a. (i) (ii) (iii) How did you do? View Answer. 9. Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost. And so we get the answer: X1 k=1 4 1 6 k = 24 5 4 = 4 5 [4] 10. In the row below, row 2, we write two 1’s. 4 Infinite Figure 2. (2) (Total 6 marks) 4. Graduate. 002 ∴ x = 0. (click to see video) One interesting example is the Fibonacci sequence. Evaluate. $\endgroup$ – Oct 11, 2016 · It is not currently accepting answers. 1 Key Facts: Informal Binomial Expansion A binomial is a polynomial that is the sum of two terms (e. Use your expansion to estimate the value of (1. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Three consecutive terms of an arithmetic series are a, b, and (3a + 4) respectively. x, of the binomial expansion Free Binomial Expansion Calculator - Expand binomials using the binomial expansion method step-by-step Apr 6, 2018 · C2 Sequences & Series: Binomial Expansion PhysicsAndMathsTutor. in the expansion. (2) (Total 9 marks) (b) The first four terms of the binomial expans ion of in ascending powers of x are 1 + ax + bx 2 + cx 3. Solution: ( 2 +x a ) 3 has coefficients 1 3 1 The circled number is the coefficient of the term 21 (x a ) 2. 10 Arithmetic Series: Finding a and d. giving each term in its simplest form. [4] Showing top 8 worksheets in the category - Binominal Expansion. 0. r. Find the first 3 terms, in ascending powers of x, of the binomial expansion Jun 20, 2020 · C2 Sequences Series: Binomial Expansion Edexcel Internal Review 1 1 a Find the first 4 terms in ascending powers of x of the binomial expansion of 1 + ax7 where a is a constant&#8230; May 27, 2024 · Get Sequences and Series Multiple Choice Questions (MCQ Quiz) with answers and detailed solutions. Notice that this corresponds to picking the first two terms from the binomial theorem expansion (1 + x)n = 1 +(n1) x +(n2) x2 + ⋯ +xn. a . 3: Geometric Sequences and Series A geometric sequence, or geometric progression, is a sequence of numbers where each successive number is the product of the previous number and some constant r . You should know that (a + b)² = a² + 2ab + b² and you should be able to work out that (a + b)³ = a³ + 3a²b + 3b²a + b³ . (b) Use your expansion to estimate the value of (1. Consider an arithmetic sequence with kth term given by a k = a+ (k 1)d. 1 Binomial Expansion for the OCR A Level Maths: Pure syllabus, written by the Maths experts at Save My Exams. (2) b. Experienced, full-time, online tutor. Find the first 4 terms, in ascending powers of x, of the binomial expansion of. Revision notes on 4. AQA Core 2 5. Book Tutor. 025-0. University of Bristol - MEng Mechanical and Electrical Engineering. 001 2) Substitute in the x value into the Expansion. ( a + b) 5. May 1, 2024 · Then, Binomial distribution is a Taylor expansion of a binomial (q + p)n where n (# of trials) is the order of interest, and r (# of successes) is the parameter defining the dominating term through. 10C6 a4b6 = 10C4 a4b6 10 × 9 × 8 × 7 4 =. For problems 3 and 4 write down the first four terms in the binomial series for the given function. 4. uk Edexcel Internal Review 1 1. C2 Sequences & Series: Binomial Expansion PhysicsAndMathsTutor. Some of the worksheets displayed are Binomial expansion work, The binomial expansion, Binomial expansion question work, Sequences and series part 1b binomial expansion, The binomial theorem, Binomial expansions exam questions, Work the binomial theorem, C2 the binomial theorem work Maths/Physics Examiner Who Has Helped 6 GCSE/IB & 8 A Level Students Acheive A*'s In Last Year Alone. 14a= 1 + 4x+ 6x2+ 4x3+ xb= 1 − 5x+ 10x− 10x3+ 5x4−x5. . All C3 Revsion Notes. The larger the power is, the harder it is to expand expressions like this directly. Here is a set of practice problems to SEQUENCES AND SERIES Answers - Worksheet C. ξ1 − 2 2, Example 1: Find the expansion of up to and including the term in and state of values for for which the expansion is valid. This topic is included in all papers for AS-level and A-level OCR (MEI) Maths. in this expansion is 525, (b) find the possible values of C2 - Sequences and Series OCR, AQA, Edexcel 1. pdf), Text File (. Dec 11, 2010 · C2 Sequences Series: Binomial Expansion PhysicsAndMathsTutor. 4 3 + x(1 12 ) in ascending powers of up to and including the x term in x3 is 1 + 9x + px2 + qx3, 12x < 1. 1 Binomial Expansion for the AQA A Level Maths: Pure syllabus C2 SEQUENCES AND SERIES Answers - Worksheet D page 4 Solomon Press 13 a12 + 12(3 = 311)(− 3 x) + 12 11 2 × (310)(− 3 x)2 + 12 11 10 32 ×× × (39)(− 3 x)3 + … = 531 441 − 708 588x + 433 026x2 − 160 380x3 + … b let 3 x = 0. May 17, 2017 · Divergence simply means "not convergence". [2] 10. (1+3x)−6 ( 1 + 3 x) − 6 Solution. Infinite Geometric Series , where we add all of the terms in the geometric progression. a4b2 term of (2a + b)6. Now, the Binomial Theorem required that n n be a positive integer. To generate Pascal’s Triangle, we start by writing a 1. txt) or read online for free. 5E. a) Binomial Expansion 1 b) Binomial Expansion 2, c) Geometric Sequences 1 ,d) Geometric Sequences 2. Nov 17, 2022 · This page titled 7: Sequences and Series, Mathematical Induction, and the Binomial Theorem is shared under a CC BY-NC-SA 3. This question is missing context or other details : Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. In the previous chapter (but not only), we also have explained how to expand the square and the cube of a binomial. This expansion is only valid when. c= 1 + 3(4x) + 3(4x)2+ (4x)3d= 1 + 3(−2y) + 3(−2y)2+ (−2y)3. 3 (i) Find and simplify the first four terms in the binomial expansion of (1 + x) 10. All C4 Revsion Notes. Find the common difference and the first term. We call these numbers the terms of the sequence. Show Solution. 15. June 2010 qu. (i) Given that . We denote the terms in a sequence by Video answers for all textbook questions of chapter 14, Binomial Expansions, Sequences, and Series, Beginning and Intermediate Algebra by Numerade Get 5 free video unlocks on our app with code GOMOBILE C2 SEQUENCES AND SERIES Answers - Worksheet C 1 4a = 1 + 4x + 6x 2 + 4x3 + x b = 1 − 5x + 10x − 10x3 + 5x4 − x5 c = 1 + 3(4x) + 3(4x)2 + (4x)3 d = 1 + 3(−2y) + 3(−2y)2 + (−2y)3 = 1 + 12x + 48x2 + 64x3 = 1 − 6y + 12y2 − 8y3 e = 1 + 4(1 2 x) + 6(1 2 x)2 + 4(1 2 x)3 + (1 2 x)4 f = 1 + 3(1 3 y) + 3(1 3 y)2 + (1 3 y)3 = 1 + 2x + 3 2 C2 SEQUENCES AND SERIES Answers - Worksheet A 1 a r = 3 b r = 1 4 c r = −2 u8 = 3 × 3 7 = 6561 u 8 = 1024 (a) Find the first four terms, in ascending powers of x, in the binomial expansion of 5. 0 license and was authored, remixed, and/or curated by Carl Stitz & Jeff Zeager via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. The Binomial Theorem, where we learn how to expand expressions like. 99812, giving your answer to 2 decimal places. x7 term of (x − 3)9. 0000065104166. C2 SEQUENCES AND SERIES Answers - Worksheet C 1 4a = 1 + 4x + 6x 2 + 4x3 + x b = 1 − 5x + 10x − 10x3 + 5x4 − x5 c = 1 + 3(4x) + 3(4x)2 + (4x)3 d = 1 + 3(−2y) + 3(−2y)2 + (−2y)3 = 1 + 12x + 48x2 + 64x3 = 1 − 6y + 12y2 − 8y3 e = 1 + 4(1 2 x) + 6(1 2 x)2 + 4(1 2 x)3 + (1 2 x)4 f = 1 + 3(1 3 y) + 3(1 3 y)2 + (1 3 y)3 = 1 + 2x + 3 2 To get an approximation you can consider a few terms from the expansion. 1. x) + 6(1 2. Show Step-by-step Solutions In the previous chapter (but not only), we also have explained how to expand the square and the cube of a binomial. (a + b) 2 = a 2 + 2ab + b 2. 2 + x k , where k is a constant. 4. Formula Book. 0 license and was authored, remixed, and/or curated by Anonymous via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. 1) Set the expansion expression equal to the new value. The binomial expansion of . The first two numbers in the Fibonacci sequence are 1, and each successive term is the sum of the previous two. y3 term of (y + 5)4. Find the first 3 terms, in ascending powers of x, of the binomial expansion of binomial theo - Free download as PDF File (. The exponents on a decrease by one on each term going left to right. 1 −. 6352 (NP: If it only mentions to use y terms in the question, you only need to add together y terms in the answer) C2 Sequences & Series: Binomial Expansion PhysicsAndMathsTutor. 1 Binomial Expansion for the AQA A Level Maths: Pure syllabus, written by the Maths experts at Save My Exams. --> (2+5x)⁹ = 2. 588 936 − 0. 528 Chapter 8 Sequences , Series , and Probability. C2 SEQUENCES AND SERIESAnswers - Worksheet C. Taking bookings for study leave, summer and 2024-2025. Prove that S = Xn k=1 a k = 1 2 n(2a+ (n 1)d): [8] Hint: this is a proof that you may have seen in class. Find the value of (2) 4a. ds lr kz dq hf nb yi nc zd yk