Problem 8. Determine whether the series is convergent or divergent by expressing as atelescoping sum. If it is convergent, find its sum.∞(a) ► v/2.n=1(b)n=1∞(c) Σn=1n³ - 2n + 12n³ +41n² + 4n+ 3(4) Σ(006 2/3 - 006 (12 +17²2)COSCOSn²(nn=1

We shall do the first three questions, for the fourth question please repost it again.We have, (a)…

Answered: Problem 8. Determine whether the series…

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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Let p(x) be the sum of the first five nonzero terms of the Maclaurin series of (1+ x) cos(2.x), then p(1) = 4 (a) 3 (b) 2 1 (c) 3 - (d) 0 2 (e) -3
If the nth partial sum of a series find an S₁ and a₁ an Σa, an n = 1 = = = = n - 3 n + 3 Σ an n = 1 n = 1 (for n = 1) is
∞ 1. Let an be a POSITIVE infinite series (i.e. an > 0 for all n ≥ 1). Let ƒ be a continuous function n=1 with domain R. Is each of these statements true or false? If it is true, prove it. If it is false, prove it by providing a counterexample and justify that is satisfies the required conditions.
2. DETAILS PREVIOUS ANSWERS Which of the following is the power series for arctan(x²) dx ? HINT: The table of series from the first question may be useful here. 22n+4 C + (-1)". (2n + 1)(2n + 4) n=0 00 x4n+3 C +>(-1)". (2n + 1)(4n + 3) C +£ (-1)",2n n=0 in+2 C+>(-1)". (2n + 1) n=0 00 2n+2 C +> (-1)"- (2n + 1)(2n + 2) n=0 gán+1 C+(-1)" (4n +2) 00 (2n + 1) n=0
Y.7.
4. It can be shown using material from a later section that Set ² d da is given by (−1)na²n+1 n!2n (2n + 1) n=0 for any positive value of a. When a is positive, this series is an alternating series. (a) Approximate dx to four decimal places accuracy by using the Alternating Series Test and its remainder theorem. (Be careful to not round intermediate steps.) (b) Using the same number of terms as you used in your sum in part (a), compute the midpoint approximation Mn for the integral fe-t³² da (c) Which approximation is more accurate? This should be determined using just parts (a) and (b).
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Problem 8. Determine whether the series is convergent or divergent by expressing as a telescoping sum. If it is convergent, find its sum. (α) Σ 12. n=1 (b) n=1 (Σ n=1 (α) Σ n=1 η3 – – 2n + 1 2n3 + 4 1 η2 + 4n + 3 COS 1 η2 COS 1 (n + 1)2