I know a lot of techniques to show that a serie converge or diverge (Cauchy condensation test, Abel's test, comparision with an integrale, root test, ratio test...).
On the other hand I know nothing about caculating the value of a serie. Is there any theorems that may help ?
From now on I know the following :
- integrale test can be combine with squeeze theorem
- geometric serie
For example in this [How to prove $\lim \limits_{x \to 1^-} \sum\limits_{n=0}^\infty (-1)^nx^{n²} = \frac{1}{2} \ $? there are talking about :
- Herglotz' trick
Weierstrass products.
...
So I would like to know if there are some other nice theorem or slick techniques to find the value of a serie.
Thank you !