0 votes 0 votes Let $n$ and $k$ be integers with $1 \leq k \leq n.$ Show that $\displaystyle{}\sum_{k=1}^{n} \binom{n}{k}\binom{n}{k − 1} = \dfrac{\binom{2n + 2}{n + 1}}{2} − \binom{2n}{n}.$ Combinatory kenneth-rosen discrete-mathematics counting binomial-theorem descriptive + – admin asked Apr 30, 2020 admin 230 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.