Yet another sum of series – math.stackexchange.com

I need to show that for some $k\in\mathbb{N}, |a|<1,$ $$\sum_{i=0}^\infty {k+i \choose k}a^i=\frac1{(1-a)^{k+1}}.$$ It's technically a power series in $a$ but no approach in that direction proved ...

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