Math Wiki

A geometric sequence is a sequence in the form

Where r is a common ratio. If , the sequence is convergent, and has a defined limit. If , the sequence is divergent, and will have an undefined limit. An example of a convergent sequence is

which will converge to 0.

A geometric series is the sum of a geometric sequence. The sum of the series is equal to

If a geometric series is infinite and convergent, the formula will still apply (again, if , the series is convergent), but since

we can use the latter formula. For example,