I came across a sum I needed to compute for a question but I wasn't able to evaluate it manually ( I ended up using Wolfram ).
\begin{equation} \sum_{n=0}^{\infty} [1000(2+0.5n)e^{-0.4n}] \end{equation}
I was curious however if there was a technique to evaluate or approximate the value of the sum (such that I didn't need a computer to do it for me). Any help would be greatly appreciated! (Note: The sum evaluated to 9150.15)