Question

Find the sum of the following infinite geometric series, if it exists.

Answer 1

I think the answer is C. 1/3

Answer 2

@Owlcoffee

Answer 3

You are correct.

Answer 4

Thank you :)

Answer 5

the sum is clearly larger than 1/3

Answer 6

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

\[3S-S=1\]
\[2S=1\]
\[S=\frac{1}{2}\]

Answer 7

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