Question

Докажите тождество:
$C^{m}_{n}+C^{m}_{n+1}+C^{m}_{n+2}+...+C^{m}_{n+m-1}=C^{m+1}_{n+m}$

Answer 1

Объяснение:

$\displaystyle C^m_n+C^m_{n+1}+C^m_{n+2}+...+C^m_{n+m-1}=\sum^{m-1}_{p=0}C^m_{n+p}=\sum^{n+m}_{s=m}C^m_s=[p=s-m]=\\ \\ \\ =\sum^{n+m-m}_{p=0}C^{m+1}_{p+m}=C^{m+1}_{n+m}$