Answered: п(x — 5)" 32n n=2 interval of…

п(x — 5)" 32n n=2 interval of convergence = (Enter your answer as an interval: thus, if the interval of convergence were –3 < x < 5, you would ente (-3,5]. Use Inf for any endpoint at infinity.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 49E

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Question

Find the interval of convergence for the power series

n(x
- 5)n
32n
n=2
interval of convergence =
(Enter your answer as an interval: thus, if the interval of convergence were –3 < x < 5, you would enter
(-3,5]. Use Inf for any endpoint at infinity.)

Expert Solution

Step 1) Find the interval of convergence for the power series

The given power series is

$\sum_{n = 2}^{\infty} \frac{n {(x - 5)}^{n}}{3^{2 n}}$

$\Rightarrow a_{n} = \frac{n {(x - 5)}^{n}}{3^{2 n}}$

by the ratio test is power series is convergent then

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