What is the sum of the infinite geometric series 2+2/3+2/9+2/27+...?

1 Answer
Jun 22, 2016

3

Explanation:

a geometric series can be defined as: an=a1(r)n1 where a1 is the first value of the series and r is the common ratio.

The common ratio is 13 and the first term is 2 so our series is:

an=2(13)n1

You can only sum an infinite geometric series if it is convergent, that is, that it converges to one value. A series is convergent if |r|<1 which in this case it is.

The equation to sum an infinite series is: a11r so by plugging all values we get: 2113 which is 223 or 62 which simplifies to 3