Binomial equation

Question

I need to prove the following equation:

$\sum_{j=k}^n \binom{j}{k} = \binom{n+1}{k+1}$

for this equation i need to suggest both algebric and combinatorial explanation.

the only thing I came up with:

as for the right side, combinatorial explanation could be number of ways for choosing subsets of k+1 people out of a n+1 people in total.

left side, though, doesnt work out for me at all.

Thanks in advance.