proof by induction that $sum_{k = n}^{m} binom{k}{n} = binom{m + 1}{n + 1}$

I am unable to solve following proof by induction.

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

Can you please help me ?

a) show that it is true for $n=m$

b) show that it is true for $(m+1,n)$

c) give proof why it works for all other values of $m,n$

Thanks.