Question 113
For every integer $n \ge 2$ prove the inequality
$$
\frac{1}{2!} + \frac{2}{3!} + \dots + \frac{2^{n-2}}{n!} \le \frac{3}{2},
$$
where $k! = 1 \cdot 2 \cdot \dots \cdot k$.
$$
\frac{1}{2!} + \frac{2}{3!} + \dots + \frac{2^{n-2}}{n!} \le \frac{3}{2},
$$
where $k! = 1 \cdot 2 \cdot \dots \cdot k$.