Question

4. Find the sum of each of the following series if they converge. $\sum_{n=0}^\infty (-1)^n \frac{\pi^{2n+1}}{4^{2n+1}(2n+1)!}$ $\sum_{n=0}^\infty (-1)^n \frac{1}{n!}$ $\sum_{n=0}^\infty (-1)^n \frac{(\sqrt{3})^{2n+1}}{2n+1}$ $\sum_{n=0}^\infty (-1)^n \frac{1}{4^n (2n)!}$

          4. Find the sum of each of the following series if they converge.
$\sum_{n=0}^\infty (-1)^n \frac{\pi^{2n+1}}{4^{2n+1}(2n+1)!}$
$\sum_{n=0}^\infty (-1)^n \frac{1}{n!}$
$\sum_{n=0}^\infty (-1)^n \frac{(\sqrt{3})^{2n+1}}{2n+1}$
$\sum_{n=0}^\infty (-1)^n \frac{1}{4^n (2n)!}$

4. Find the sum of each of the following series if they converge.
∑n=0^∞ (-1)^n (π^2n+1)/(4^2n+1(2n+1)!)
∑n=0^∞ (-1)^n (1)/(n!)
∑n=0^∞ (-1)^n ((√(3))^2n+1)/(2n+1)
∑n=0^∞ (-1)^n (1)/(4^n (2n)!)

Added by Linda N.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

08/17/2023

Step 1

Step 1: For series (a), we have 8 * Tr2n+1 * (-1)^n * 42n+1 * (2n+1)!. Show more…

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4. Find the sum of each of the following series if they converge 8 Tr2n+1 (a) (-1)n 42n+1(2n+1)! n=0 (V3)2n+1 (c) (-1)n 2n+1 n=0 8 8 1 (b) C(-1)m iu n=0 (d) Z(-1)m 4n(2n)! n=0