Even and odd coefficient sums for JEE

Formula

\[\sum_{\substack{r=0\\ r\text{ even}}}^{n}{n\choose r}=\sum_{\substack{r=0\\ r\text{ odd}}}^{n}{n\choose r}=2^{n-1}\quad (n\ge 1)\]

Variables: \(n\) is a positive integer.

Separating even and odd terms in binomial expansions.