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Question Number 120875 by mnjuly1970 last updated on 03/Nov/20

$$...\mathcal{N}icecalculus...$$$$$$$$evaluate::$$$$S=\underset{n=1}{\sum ^{\mathrm{\infty }}}\left(\frac{2^{-2n}}{1+cos\left(\frac{\pi }{2^n}\right)}\right)=??$$$$...\mathcal{M}.\mathcal{N}.1970...$$

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