range of x

Dec 2015
972
128
Earth
Find the range of x such that :
\(\displaystyle e^{-x} H_x > e^{-x^2 }H_{x^2 }\; \) , \(\displaystyle x\in \mathbb{N}\).

\(\displaystyle e^{-x} \left( 1+1/2+...+1/x \right) > e^{-x^2 } \left(1+1/2+...+1/x^{2}\right)\).
 
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