How do I find the sum of the infinite geometric series $2/3$ , $- 4/9$ , ...?

Question

4638 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-10-17T21:54:11

Recall: Geometric Series

$a+ar+ar^2+ar^3+cdots=a/{1-r}$ if $|r|<1$ .

Let us look at the posted geometric series,

$S=2/3-4/9+8/27-cdots$

by rewriting a bit to fit the form of geometric series,

$=2/3+2/3(-2/3)+2/3(-2/3)^2+cdots$

since $a=2/3$ and $r=-2/3$ ,

$={2/3}/{1-(-2/3)}=2/5$

I hope that this was helpful.

How do I find the sum of the infinite geometric series 2/32/3, - 4/9- 4/9, ...?