Possible Duplicate:
Summation of $\sum\limits_{n=1}^{\infty} \frac{x(x+1) \cdots (x+n-1)}{y(y+1) \cdots (y+n-1)}$
Through a numerical computation, I stumbled across the following identity. It takes place in the ring $(\mathbb{Z}[x])[[t]]$, which is complete with respect to the $t$-adic valuation. The apparent identity is $\sum_{n=0}^\infty\frac{x(x+1)(x+2)\cdots(x+n-1)}{(1+t)(1+2t)\cdots(1+nt)}t^n=\frac1{1-xt}$
I have numerically verified that this holds $\bmod t^{50}$. Does anyone have any ideas about how to prove this identity?