   Chapter 11.7, Problem 8E

Chapter
Section
Textbook Problem

# Test the series for convergence or divergence.8. ∑ n = 1 ∞ ( − 1 ) n − 1 n 4 4 n

To determine

Whether the series convergence or divergence.

Explanation

Result used: The Ratio Test

(i) If limn|an+1an|=L<1, then the series n=1an is absolutely convergent (and therefore convergent.)

(ii) If limn|an+1an|=L>1 or limn|an+1an|=, then the series n=1an is divergent.

(ii) If limn|an+1an|=1, the Ratio Test inconclusive; that is, no conclusion can be drawn about the convergence or divergence of n=1an.

Calculation:

The given series n=1an=n=1(1)n1n44n.

Then, the (n+1) th term is, an+1=(1)n(n+1)44n+1.

Obtain the limit of |an+1an|

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