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**Glitch** Determine if the following alternating series converges. Is it absolutely convergent?

$\displaystyle \sum\limits_{k = 3}^\infty \frac{(-1)^k}{ln(k)}$

Using the alternating series test, we need:

a) $\displaystyle a_k \ge 0$

b) $\displaystyle a_{k} \ge a_{k + 1}$

c)$\displaystyle \lim\limits_{k \to \infty} a_k = 0$

a) $\displaystyle \frac{1}{ln(k)}$ > 0 for all k > 1

b) $\displaystyle \frac{1}{ln(k)} \ge \frac{1}{ln(k+1)}$ for all k > 1

c) Limit is obviously 0 as $\displaystyle k \to \infty$

Thus the series converges.