   Chapter 11.7, Problem 24E

Chapter
Section
Textbook Problem

# Test the series for convergence or divergence.24. ∑ n = 1 ∞ n sin ( 1 / n )

To determine

To test: Whether the series convergence or divergence.

Explanation

Result used:

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

Calculation:

Consider the given series n=1an=nsin(1n), where an=nsin(1n).

Obtain the limit an.

limnan=limn[nsin(1n)]=limnsin(1n)(<

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