Transformation in convergence of series

Question

I have a small problem with the correction of one of the exercises in my mid-term exam. Please have a look at the screenshot below:

Convergence of series exercise (c)

I understand why the quotient criterion was used and everything else as well, but what I don't get is the last expression. I do not see exactly how the $\exp(n-1)$ is gone ... Where did it go?

Answer 1

Hint: $$\frac{e^{n-1}}{e^n}=e^{n-1-n}=e^{-1}=\frac{1}{e}$$