Mathematical induction on binomial coefficients I need to prove the following statement (Pascals Identity) on binomial coefficients using mathematical induction only
$$\binom{n}{r} = \binom{n-1}{r}+\binom{n-1}{r-1}$$
My doubt is
Whether I need to prove the following two statements or only the first one?
$$\binom{n+1}{r} = \binom{n}{r}+\binom{n}{r-1}$$
$$\binom{n}{r+1} = \binom{n-1}{r+1}+\binom{n-1}{r}$$

For Mathematical induction, you prove $$\binom{n}{r} = \binom{n-1}{r}+\binom{n-1}{r-1}$$ 
for $n=1$.
Then assume that $$\binom{n}{r} = \binom{n-1}{r}+\binom{n-1}{r-1}$$ is true for $n=k$, and prove it for $n=k+1$
You do not need to change $r$ to $r+1$
This problem may be easier to solve without Mathematical Induction, but it is your choice. 
