MathDB
Binomial coefficients everywhere

Source: Indonesian Mathematical Olympiad 2014 Day 2 Problem 7

September 4, 2014
algebrapolynomial

Problem Statement

Suppose that k,m,nk,m,n are positive integers with k≤nk \le n. Prove that: ∑r=0mk(mr)(nk)(r+k)(m+nr+k)=1\sum_{r=0}^m \dfrac{k \binom{m}{r} \binom{n}{k}}{(r+k) \binom{m+n}{r+k}} = 1
Back to ProblemsView on AoPS