summation - Find the following limit: $limlimits_{n to infty}(e-1)sum_{k=1}^n frac{1}{n+k(e-1)}$

I'm having problems with the following limit:

$\lim\limits_{n \to \infty}(e-1)\sum_{k=1}^n \frac{1}{n+k(e-1)}$

It's a task from a taskbook for first year engineering students. Any help is appreciated. Thanks.