# Geometric series

This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
Important to fix up! Currently just notes

## Notes

For the geometric progression [ilmath](1,r)[/ilmath] we have:

• $S_n:\eq\sum^n_{k\eq 1}r^{k-1}\eq\frac{1-r^n}{1-r}$ (with first term [ilmath]n\eq 1[/ilmath], as is our convention (see: sequence))

Thus for a general geometric progression, [ilmath](a,r)[/ilmath] we have:

• $S_n:\eq\sum^n_{k\eq 1}ar^{k-1}\eq a\sum^n_{k\eq 1}r^k{-1}\eq a\frac{1-r^n}{1-r}$