   Chapter 11.5, Problem 2E

Chapter
Section
Textbook Problem

# Test the series for convergence or divergence.2. 2 3 − 2 5 + 2 7 − 2 9 + 2 11 − ⋯

To determine

To test: Whether the series is convergent or divergent.

Explanation

Given:

The series is 2325+2729+211 .

Result used:

“If the alternating series n=1(1)n1bn=b1b2+b3b4+...   bn>0 satisfies the conditions bn+1bn   for all n and limnbn=0 , then the series is convergent; otherwise, the series is divergent.”

Calculation:

The given series can be expressed as follows,

2325+2729+211=2(2(1)+1)2(2(2)+1)+2(2(3)+1)2(2(4)+1)+2(2(5)+1)=n=1(1)n+12(2n+1)

Consider the given series n=1bn=n=1(1)n+12(2n+1) , where bn=22n+1

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