Problem

Source: Mongolia TST 2011 Test 4 #1

Tags: inequalities unsolved, inequalities



Let $t,k,m$ be positive integers and $t>\sqrt{km}$. Prove that $\dbinom{2m}{0}+\dbinom{2m}{1}+\cdots+\dbinom{2m}{m-t-1}<\dfrac{2^{2m}}{2k}$ (proposed by B. Amarsanaa, folklore)