Each of two summands decreases. It is equivalent to the fact that $(e^x-1)/x$ increases, and this follows from the convexity of exponent: if $f$ is convex, then $(f(x)-f(a))/(x-a)$ increases as a function of $x$ for fixed $a$, apply this to $f(x)=e^x$ and $a=0$.
Fedor Petrov
- 108.9k
- 9
- 264
- 459