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## Main Question or Discussion Point

**Algorithms for infinite geometric series via long division??**

I can't seem to find any algorithms for this on the internet easily.

If I have a function of the form [tex]f(x)=\frac{a}{x+b}[/tex] there should be an algorithm I can use to find some terms of the corresponding series [tex]\sum _{n=0}^{\infty}\frac{a}{b}\left(\frac{-x}{b}\right)^n[/tex]

I can't seem to comprehend how to carry out the division for something like that; obviously it's not absolutely necessary if you know how to find the series using long division, but saw this worked out before and couldn't make sense of it. How does it work?