Could the limit be obtained by a Riemann sum?

Question

For $0<s<1$ and $n=1,2,\dots$, let $\Delta_n=1/(2n)$, $x_k=\frac{1}{2}+\frac{k}{2n}$ and $$ a_n=\sum_{k=0}^{n-1}\frac{\Delta_n}{x_k}e^{\frac{-s\Delta_n}{x_k}}. $$ Then, could we think of $a_n$ as a Riemann sum so as to obtain that $$ \lim_{n\to\infty}a_n=\int_{1/2}^{1}\frac{1}{x}e^{\frac{-s}{x}}dx? $$ However, it seems strange when dealing with the exponent in $a_n$. It is possible to derive the limit (as an integral) in this way? Please give me some help. Thanks a lot.