MathDB

Let

r

and

n

be nonnegative integers such that

r \le n

(a)

Prove that: \frac{n\plus{}1\minus{}2r}{n\plus{}1\minus{}r} \binom{n}{r} is an integer.

(b)

Prove that: \displaystyle\sum_{r\equal{}0}^{[n/2]}\frac{n\plus{}1\minus{}2r}{n\plus{}1\minus{}r} \binom{n}{r}<2^{n\minus{}2} for all

n \ge 9

Problem Statement