Chapter 9.8, Problem 27E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Finding the Interval of Convergence In Exercise 15-38. find the Interval of convergence of the power series. (Be sure in include a check for convergence at the endpoints of the interval.) ∑ n = 0 ∞ ( − 1 ) n + 1 ( x − 1 ) n + 1 n + 1

To determine

To Calculate: The Interval of convergence for the power series n=0(1)n+1(x1)n+1n+1.

Explanation

Given:

The power series is âˆ‘n=0âˆž(âˆ’1)n+1(xâˆ’1)n+1n+1.

Formula Used:

By ratio test, the series is convergent if

limnâ†’âˆž|un+1un|<1

Calculation:

Consider the power series,

âˆ‘n=0âˆž(âˆ’1)n+1(xâˆ’1)n+1n+1

The nth term of the series is

un=(âˆ’1)n+1(xâˆ’1)n+1n+1

The (n+1)th term of the series is

un+1=(âˆ’1)n+2(xâˆ’1)n+2n+2

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