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Alternating Series Test Show that the series
Chapter 10, Problem 48E(choose chapter or problem)
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?
Questions & Answers
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