Hello,

I was wondering if anyone could help me show the following:

$\displaystyle \displaystyle\sum_{i=1}^n\frac{(t+n-1)!(i-1)!}{(t+i-1)!}=\frac{(n+t-1)!-n!}{(t-1)!(t-1)}$,

where $\displaystyle t\geqslant2$.

It's an important part of a larger problem I'm working on and I'm a little stuck.

Thanks in advance.