## anonymous one year ago Find the sum of the following infinite geometric series, if it exists.

1. anonymous

2. anonymous

I think the answer is C. 1/3

3. anonymous

@Owlcoffee

4. Owlcoffee

You are correct.

5. anonymous

Thank you :)

6. Zarkon

the sum is clearly larger than 1/3

7. Zarkon

it is geometric and clearly converges...therefore...let $S=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\cdots$ $3S=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\cdots$ $3S-S=1$ $2S=1$ $S=\frac{1}{2}$

8. Owlcoffee

Yes, I did the math yesterday and found I was incorrect. Thanks Zarkon.