Greatest value of the binomial coefficient.

Question

How should I prove the greatest value of the binomial coefficient $C(n,r)$ occurs for $r=\left[\cfrac{(n+1)}{2}\right]$ ?

Answer 1

To find the maximum binomial coefficient consider x=a=1.By the above theorem max term will give us the max binomial coefficient. r=[n+1/1+1]=[n+1/2]

Answer 2

Note that $C(n,r+1)=C(n,r)\cdot\frac{n-r}{r+1}$.

Answer 3

HINT: Look at Pascals' Triangle. Notice where the maximum values of each row occur.