We have the following sum:
$$\displaystyle \sum_{n=4}^\infty \dfrac{(-1)^n}{\log(\log(n))} $$
I have a hunch this series is conditionally convergent, but I get nowhere using the ratio test. What test would be best to apply to this particular series?
2025-01-13 00:02:49.1736726569
Convergence/divergence of the series $\sum_{n=4}^\infty\frac{(-1)^n}{\log(\log(n))}$?
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You may just use the alternating series test:
the function $x \mapsto \dfrac{1}{\log(\log(x))}$ is decreasing,
as $x \to \infty$, you have $\dfrac{1}{\log(\log(x))} \to 0.$