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Activity 8.4.6 .
(a)
Consider the series \(\sum (-1)^k \frac{\ln(k)}{k}\text{.}\)
Does this series converge? Explain.
Does this series converge absolutely? Explain what test you use to determine your answer.
(b)
Consider the series \(\sum (-1)^k \frac{\ln(k)}{k^2}\text{.}\)
Does this series converge? Explain.
Does this series converge absolutely? Hint: Use the fact that
\(\ln(k) \lt \sqrt{k}\) for large values of
\(k\) and then compare to an appropriate
\(p\) -series.
