Question 438222
{{{S = a + ar + ar^2 }}}+...+{{{ar^(n-2) + ar^(n-1)}}}
=a({{{1 + r + r^2 }}}+...+{{{r^(n-2) + r^(n-1)}}})

=a({{{1 + r + r^2 }}}+...+{{{r^(n-2) + r^(n-1)}}})*{{{((1-r)/(1-r))}}}
=a*{{{(1-r^n)/(1-r)}}}

This formula is valid only when |r| < 1.