Science:Math Exam Resources/Courses/MATH101 A/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

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

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