Alternating Series Test Show that the series

Chapter 10, Problem 48E

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QUESTION:

Alternating Series Test Show that the series

\(\frac{1}{3}-\frac{2}{5}+\frac{3}{7}-\frac{4}{9}+\cdots=\sum_{k=1}^{\infty}(-1)^{k+1} \frac{k}{2 k+1}\)

diverges. Which condition of the Alternating Series Test is not satisfied?

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QUESTION:

Alternating Series Test Show that the series

\(\frac{1}{3}-\frac{2}{5}+\frac{3}{7}-\frac{4}{9}+\cdots=\sum_{k=1}^{\infty}(-1)^{k+1} \frac{k}{2 k+1}\)

diverges. Which condition of the Alternating Series Test is not satisfied?

ANSWER:

Solution:-Step1Given that Step2To findShow that the series Step3Let Also,Di

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