How to prove the Taylor series identity

Question

How to prove the following identity: $(1-t)^{-L}=\sum_{j\geq 0} \binom{j+L-1}{L-1}t^j$.

I will appreciate for your helpful suggestion.

Answer 1

HINT

Refer to the Binomial Series

$$(1 + x)^\alpha = \sum_{k=0}^{\infty} \; {\alpha \choose k} \; x^k $$

for the special case with negative integer exponent.