Question 123
Let $t$, $k$, $m$ be positive integers and $t \gt \sqrt{km}$. Prove that
$$ \binom{2m}{0} + \binom{2m}{1} + \dots + \binom{2m}{m-t-1} \lt \frac{2^{2m}}{2k}. $$
(proposed by B. Amarsanaa, folklore)
$$ \binom{2m}{0} + \binom{2m}{1} + \dots + \binom{2m}{m-t-1} \lt \frac{2^{2m}}{2k}. $$
(proposed by B. Amarsanaa, folklore)