   Chapter 11.6, Problem 36E

Chapter
Section
Textbook Problem

# Use any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent.36. ∑ n = 1 ∞ sin ( n π / 6 ) 1 + n n

To determine

Whether the series is absolutely convergent or conditionally convergent.

Explanation

Given:

The series is n=1sin(nπ6)1+nn.

Definition used:

“A series an is called absolutely convergent if the series of absolute values |an| is convergent.”

Result used:

(1) “Suppose that an and bn are the series with positive terms,

(a) If bn is convergent and anbn for all n, then an is also convergent.

(b) If bn is divergent and anbn for all n, then an is also divergent.”

(2) The p-series n=11np is convergent if p>1 and divergent if p1

Calculation:

Consider the given series n=1an=n=1sin(nπ6)1+nn where an=

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