Question 1013967
.
What is the sum of this infinite geometric series  1 - 1/3 + 1/9 - . . . 
------------------------------------------------------------------


The first term is  1.
The common ratio is  {{{-1/3}}}.


Now apply the formula for the sum of an infinite geometric progression with the first term &nbsp;a&nbsp; and the common ratio &nbsp;r, &nbsp;|r| < 1 :


{{{S}}} = {{{a/(1-r)}}}.


So, &nbsp;in our case


{{{S}}} = {{{1/(1-(-1/3))}}} = {{{1/((4/3)))}}} = {{{3/4)}}}.