How to find the limit of series? (What should I know?) – math.stackexchange.com

How to find the limit of series? (What should I know?) – math.stackexchange.com

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There is a couple of limits that I failed to find: $$\lim_{n\to\infty}\frac 1 2 + \frac 1 4 + \frac 1 {8} + \cdots + \frac {1}{2^{n}}$$ and $$\lim_{n\to\infty}1 - \frac 1 3 + \frac 1 9 - \frac 1 ...

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