Geometric sequence formulas (thing)

This writeup contains "sum of an infinite geometric series" and "sum of a finite geometric sequence".
Please note that because of limitations in HTML, the "math format" doesn't look perfect, and may even look messed up, depending on your browser.

Sum of an Infinite Geometric Series
long (written out) format
(summation of a times (r to the n^th power), as n goes from 0 to infinity) equals (a divided by (1 - r)), if and only if (the absolute value of r is between 0 and 1)

math format
   ∞
  Σ   arⁿ
n = 0

      =

    a
^--------
  1 - r

      iff

0 < |r| < 1

Sum of a Finite Geometric Sequence
long (written out) format
(summation of a times (r to the (i - 1) power), as i goes from 1 to n) equals (a times (1 - (r to the n^th power)) divided by (1 - r))

math format
   n
  Σ   ar^{i - 1}
i = 1

      =

    1 - rⁿ
a ^---------
    1 - r