Let for a differentiable function f:(0, ∞) → R, f(x)-f(y) ≥ log_e (x/y)+x-y, ∀ x, y ∈(0, ∞). Then Σ_n=1^20 f^′(1/n^2) is equal to ____.

Let for a differentiable function $\displaystyle f:(0, \infty) \rightarrow \mathbf{R}, f(x)-f(y) \geqslant \log _{\mathrm{e}}\left(\frac{x}{y}\right)+x-y, \forall x, y \in(0, \infty)$. Then $\displaystyle \sum_{n=1}^{20} f^{\prime}\left(\frac{1}{n^2}\right)$ is equal to $\displaystyle \_\_\_\_$.