How do you find the sum of the infinite geometric series 1 + 1/3 + 1/9 + ....?

Question

40071 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-01T22:34:17

Use the formula for the sum of an infinite geometric series to find:

$1+1/3+1/9+... = 3/2$

The general term of a geometric series is given by the formula:

$a_n = a r^(n-1)$

where $a$ is the initial term and $r$ the common ratio.

The sum of an infinite geometric series is given by the formula:

$sum_(n=1)^oo a r^(n-1) = a/(1-r)$

when $abs(r) < 1$ . Otherwise the series does not converge.

In our current example $a=1$ and $r = 1/3$ , so we find:

$sum_(n=1)^oo (1 * (1/3)^(n-1)) = 1/(1-1/3) = 1/(2/3) = 3/2$