Chapter 9.5, Problem 70E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Using a Series In Exercises 69 and 70, use the given series.(a) Does the series meet the conditions of Theorem 9.14? Explain why or why not.(b) Does the series converge? If so, what is the sum? ∑ n = 1 ∞ ( − 1 ) n + 1 a n , a n = { 1 n , if   n   is   odd 1 n 3 , if   n   is   even

(a)

To determine
The series n=1(1)n+1an , an={1n , if n is odd1n3 , if n is even  satisfies the condition of theorem “Alternating series test” i.e. n=1(1)n+1an then series converges if the two conditions

satisfies, limnan=0 and an+1an, for all n.

Explanation

Given:

The provided series is n=1(1)n+1an , an={1n , if n is odd1n3 , if n is even .

Explanation:

The “Alternating series test” is n=1(1)n+1an then series converges if the two conditions

satisfies, limnan=0 and an+1an, for all n.

If the series have to be convergent then it must have to satisfies all the condition of “Alternating series test”

(b)

To determine
That the series n=1(1)n+1an , an={1n , if n is odd1n3 , if n is even  converges or not. If,

converges then find the sum.

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