2
$\begingroup$

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?

$\endgroup$
  • $\begingroup$ I changed $x\to n$ to have the question body agree with the title. $\endgroup$ – Winther Dec 9 '15 at 0:02
2
$\begingroup$

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 $\dfrac{1}{\log(\log(x))} \to 0.$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.