I would like to have another tutor try this one out. The number seems slightly off. Determine if each of the following series converge or diverge. If a series converges, give its sum.(a) \[\sum_{n=1}^{\infty} \frac{(-1)^{n-1} 5^{n+2}}{11^n}\]

Given,∑n=1∞-1n-15n+211nSimplifying,∑n=1∞--5n+211-nPull the constant out of the…

Answered: Determine if each 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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I would like to have another tutor try this one out. The number seems slightly off.

Determine if each of the following series converge or diverge. If a series converges, give its sum.

(a)

\[
\sum_{n=1}^{\infty} \frac{(-1)^{n-1} 5^{n+2}}{11^n}
\]

Expert Solution

Step 1

$G i v e n, \sum_{n = 1}^{\infty} \frac{{(- 1)}^{n - 1} 5^{n + 2}}{11^{n}} S i m p l i f y i n g, \sum_{n = 1}^{\infty} - {(- 5)}^{n + 2} 11^{- n} P u l l t h e c o n s \tan t o u t o f t h e s e r i e s - 25 \sum_{n = 1}^{\infty} {(- \frac{5}{11})}^{n} \sum_{n = 1}^{\infty} {(- \frac{5}{11})}^{n} i s a n i n f i n i t e g e o m e t r i c s e r i e s w i t h t h e f i r s t t e r m b = - \frac{5}{11} a n d t h e c o m m o n r a t i o q = - \frac{5}{11}$

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