Some nice theorem to find the value of serie

In this regard, series are much like integrals: you need knowledge and, even more, ingenuity and experience.

Some basic Theorems, besides those you cited, are:
- Indefinite Sum;
- Summation by parts; - (Discrete) Convolution;
- Partial Fractions Decomposition;
- Binomial Tranform and others;
- Gosper's Algorithm and Hypergeometric Function;
- Abel's Binomial Theorem
and many others

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Calculus

Sequences And Series

Real Analysis

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