A geometric series is a sequence where the there is a constant ratio between each term.

eg, the geometric sequence where the multiplier is 1/2 and the first term is 3 would look like:

Suppose we wanted to find the sum of all terms in the series. We would do:

unfortunately, you would never stop writing the sum down!

Instead, we notice that the series can be written:

Which can be expressed as a single summation

is that what you were asking? or did you want an explanation of why . in that case you might want to look at http://en.wikipedia.org/wiki/Summation