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

F i n d t h e f o l l o w i n g s u m i f i t c o n v e r g e s :

S = \underset{r = 0}{\sum^{\infty}} (\begin{matrix} 1 / 2 \\ 2 r \end{matrix}) {(- 1)}^{r}