Hey

i have to proof the following equations but not with induction and I have absolutly no idea:

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

and more general:

$\displaystyle

\sum_{j=m}^{n} {a+i \choose k} = {a+n+1 \choose k+1}-{a+m \choose k+1}\quad \forall n \in \mathbb N \quad \forall a \in \mathbb R$

Hope anyone can help me