5. (a) Determine which of the following series converge and which diverge.n³ + 2n² + 3n+1(n + 2)³(i)(ii)n=18n=18(iii) Σn=2(−1)n+1 n4n³ + 3n² + 31n(Inn)

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Answered: 5. (a) Determine which of the following…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1 (4) Find the sum of the telescoping series 2n=1 244n+3
00 (a) Starting with the geometric series xn , find the sum of the series n = 0 00 E nxn - 1, |x| < 1. n = 1 1 1-x (b) Find the sum of each of the following series. 00 (i) 2 nx", |x| < 1 n = 1 1- x 00 (ii) E Σ 6h n = 1 6. 25
2 n 9. bn is series (1) and is series (2) Find the value of (b) which If b+1 n= n=1 the summation for the two series are equal (sum1=sum2) when they are both convergent
2. Which of the following series converge conditionally? E(-1)- 2+(-1)" 3+ (-1)" O 1, 1.3 1-3-5 --- (2n – 1) +(-1 3 - 5 - 7 -- (2n + 1) 1.3.5 --+ 3' 3.5 +.. 3.5-7 E(-1)" sin n+ n=1 E(-1)" In " n+1 cos (2n)! 1.3-5 ..- (2n – 1) E(-1)"ne El-1)". Vn(n+2) 1 E(-1)"n² tan n=1
4. Find (i) a formula for the partial sum s, for each of the series below and (ii) the sum of the series, if convergent. (b) -1)"22n+l3 5n 2n 1 - (a) In 2n + 1 n=1 n=0
AQuestion Completion Status: Problem 1: Which of the following series converge by the alternating series test. Select all that apply. (-1)"n² 回》 Vn3 + 1 n=1 8 [ii] (-1)"-!el-n n=1 (-1)" [iii] ) 2+3n n=1 [iv] (-1)"n In(n) n=1 [i] [ii] [iv] Save All Answers Close Window Click Save and Submit to save and submit. Click Save All Answers to save all answers. pg.jpg MATH1132_Q11.2.pdf pg.jpg MATH1132_Q11.4.pdf MATH1132_Q11.3.pdf Essay 1 Makin....docx POF MacBook Pro
(c) Find the sum of each of the following series. (i) 2 n(n – 1)x", \x| < 1 n = 2 .2 (1–x)3 n² – n (ii) 3n n = 2 (iii) Σ 2" n = 1 8

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5. (a) Determine which of the following series converge and which diverge. n³ + 2n² + 3n+1 (n + 2)³ (i) (ii) n=1 8 n=1 8 (iii) Σ n=2 (−1)n+1 n 4n³ + 3n² + 3 1 n(Inn)