Greatest value of the binomial coefficient.

Question

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

See http://math.stackexchange.com/questions/722952/how-do-you-prove-n-choose-k-is-maximum-when-k-is-lceil-frac-n2-rceil — Martin Sleziak, Jul 28 '14 at 13:37

score 1 · Answer 1 · answered Jul 03 '14 at 12:19

1

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

answered Jul 03 '14 at 12:19

Hagen von Eitzen

score 0 · Answer 2 · answered Jul 03 '14 at 12:45

0

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

answered Jul 03 '14 at 12:45

Vishwa Iyer

score 0 · Accepted Answer · answered Jul 03 '14 at 13:45

0

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]

answered Jul 03 '14 at 13:45

Ahe

3 Answers3