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Fedor Petrov
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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