Up-front: Met the snobs on Math overflow and thought I'd try here instead. I have three STEM degrees including math, and this is for work not school; just trying to save hours googling.
This equation diverges so I can't just solve it. What I'd like to find is a way to sum a finite # of terms to a specific number of decimal places (say 4). X is a variable, c is a decimal less than 1. Ultimately, I hope to create a formula that will just calculate what I want. Any ideas?
$$\sum_{n=1}^{\infty} xc(1+c)^{n-1}$$
When $r \not= 1$, $$ \sum_{n=1}^{N} r^{n-1} = 1 + r + r^2 + \cdots + r^{N-1} = \frac{r^N-1}{r-1} = \frac{1-r^N}{1-r}. $$ That is a standard formula for a finite geometric series.