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