Geometric series

Adding powers of r forever gives a finite number when |r| < 1. History: antiquity.

\sum_{k=0}^{\infty} r^k = \frac{1}{1-r},\quad |r|<1

How to work it out

1
The statement:
$\sum_{k=0}^{\infty} r^k = \frac{1}{1-r},\quad |r|<1$
2
Adding powers of r forever gives a finite number when |r| < 1.
3
Below, the numbers in the table are computed by this site from the definition, not copied.

LaTeX source of the formulas on this page

\[ \sum_{k=0}^{\infty} r^k = \frac{1}{1-r},\quad |r|<1 \]

What is the geometric series?

Adding powers of r forever gives a finite number when |r| < 1.

Who is the Geometric series associated with?

Archimedes, Euclid.