Infinite geometric series

Find the sum of an infinite geometric series, but only if it converges!

Problem

If the following infinite geometric series converges, find its sum.
1, plus, 1, point, 2, plus, 1, point, 2, start superscript, 2, end superscript, plus, 1, point, 2, start superscript, 3, end superscript, point, point, point
Please choose from one of the following options.