Question

What is the sum of the infinite geometric series `sum_(n=1)^oo(1/3)^n` ?

Answer 1

This is a geometric series with first term `1/3` and common ratio `1/3` (see geometric series ).
The common ratio is less than 1 in absolute value, so that the series is convergent and its sum is given by `"first term"/(1-"common ratio")=(1/3)/(1-(1/3))=1/2`

You need to review geometric series Geometric Series