In this paper, we prove that for $s\in(0,\infty)$, the harmonic mean of $E_k(s)$ and $E_k(1/s)$ is always less than or equal to $\Gamma(1-k,1)$. Where generalized exponential integral function, $\Gamma(u,s)$ upper incomplete gamma function $k\in \mathbb{N}$.
