   Chapter 11.5, Problem 5E

Chapter
Section
Textbook Problem

Test the series for convergence or divergence. ∑ n = 1 ∞ ( − 1 ) n − 1 3 + 5 n

To determine

To test:

The given series is convergent or divergent

Explanation

1) Concept:

The Alternating Series Test:

If the alternating series

n=1-1n-1bn=b1-b2+b3-b4+b5-b6+, bn>0

satisfies,

i. bn+1<bn,  for all n

ii. limnbn=0

then the series is convergent.

2) Given:

n=1-1n+13+5n

3) Calculation:

The given series is in the form of an alternating series.

The given series can be written as

n=1-1n+13+5n=n=1-1n+1bn

Assume that,

bn

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