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.
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,