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Find-the-following-sum-if-it-converges-S-r-0-1-2-2r-1-r-




Question Number 1106 by 112358 last updated on 14/Jun/15
Find the following sum if it converges:  S=Σ_(r=0) ^∞  (((1/2)),((2r)) ) (−1)^r
$${Find}\:{the}\:{following}\:{sum}\:{if}\:{it}\:{converges}: \\ $$$${S}=\underset{{r}=\mathrm{0}} {\overset{\infty} {\sum}}\begin{pmatrix}{\mathrm{1}/\mathrm{2}}\\{\mathrm{2}{r}}\end{pmatrix}\:\left(−\mathrm{1}\right)^{{r}} \\ $$

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