I need to prove that: $$\sum^n_{k=0} {{k} \choose {l}} = {{n+1} \choose {l+1}}, n, l \in \mathbb{N}$$
This would look a simple sinduction proof but in that case I got a variables and I don't know what to do. Do I take my base as $n=1$ and $l=1$ and then prove for $n+1$ and $l+1$ at the same time? Or do I need to do that separately?
It looks pretty basic so I guess that there is solution somewhere on that forum, but I had no luck finding it.
