I'm on an exercise for the university and have no clue what to do. The exercise is the following: You should proof that $\sum_{i=k}^n {i \choose k}= {{n+1}\choose {k+1}}$ . I've done that with an induction over $n$ and this goes very well.
But the other part is that we should use another formula an that is the following to proof it:
$$\sum_{i=k}^n {{i+1}\choose{k+1}} = \sum_{i=k}^n {i \choose{k+1}} + {i \choose{k}}$$
And there i need your help. Does anyone know what to do with this??
Thanks for your help!