Science:Math Exam Resources/Courses/MATH101 C/April 2025/Question 08 (c)/Statement

In this question, $a$ is a real number.

Find, with justification, all values of $a$ for which the series

$$\begin{array}{r}\sum _{n=1}^{\mathrm{\infty }}{e}^n{e}^{-an}.\end{array}$$

converges. Evaluate the series (in terms of $a$ ) for all values of $a$ for which it converges.