Question 96
Let $a_1,\ldots,a_n$ be nonnegative real numbers such that for every integer $1\le k\le n$,
$$a_1a_2\cdots a_k\ge\frac1{(2k)!}.$$
Prove
$$a_1+\cdots+a_n\ge\frac1{n+1}+\frac1{n+2}+\cdots+\frac1{2n}.$$
$$a_1a_2\cdots a_k\ge\frac1{(2k)!}.$$
Prove
$$a_1+\cdots+a_n\ge\frac1{n+1}+\frac1{n+2}+\cdots+\frac1{2n}.$$