Question

nCr+1+ncr-1+2×ncr in the form of mck

Answer 1

${}^{n} C_{r+1} + {}^{n} C_{r-1} +2 {}^{n} C_{r} \\ \\ = {}^{n} C_{r+1} + {}^{n} C_{r}+ {}^{n} C_{r-1} + {}^{n} C_{r} \\ \\ = [ {}^{n} C_{r+1} + {}^{n} C_{r}]+[ {}^{n} C_{r-1} + {}^{n} C_{r}] \\ \\ = {}^{n+1} C_{r+1} + {}^{n+1} C_{r} \\ \\ = {}^{n+2} C_{r+1}\\ \\ \\ In\ \ {}^{m} C_{k} \ \ form,\\ \\ \bold{\boxed{ \red{{}^{n} C_{r+1} + {}^{n} C_{r-1} +2 {}^{n} C_{r} = {}^{n+2} C_{r+1} }}}$