How can we handle sums of the type:$$\sum_{n=0}^{\infty}\frac{1}{2^{2^n}}$$ It is different from geometric series. Is there any general approach to deal such sums?
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See also: Sum of Infinite Series $1 + 1/2 + 1/4 + 1/16 + \cdots$, How to sum this series to infinity: $\sum_{n=0}^{\infty} \frac1{2^{2^n}}$. – Martin Sleziak Aug 25 '17 at 12:26