   Chapter 11.5, Problem 4E

Chapter
Section
Textbook Problem

# Test the series for convergence or divergence.4. 1 ln 3 − 1 ln 4 + 1 ln 5 − 1 ln 6 + 1 ln 7 − ⋯

To determine

To test: Whether the series is convergent or divergent.

Explanation

Given:

The series is 1ln31ln4+1ln51ln6+1ln7

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,

1ln31ln4+1ln51ln6+=1ln(1+2)1ln(2+2)+1ln(3+2)1ln(4+2)+=n=1(1)n+11ln(n+2)

Consid

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