Thread: simple question

What is the sum of (2 to the n-1)/(3 to the n) where n goes from 1 to infinity?

In other words what is the sum of 1/3 + 2/9 + 4/27 + 8/81 ...

Originally Posted by shadow1

What is the sum of (2 to the n-1)/(3 to the n) where n goes from 1 to infinity?

In other words what is the sum of 1/3 + 2/9 + 4/27 + 8/81 ...

Hello,

use the sum formula for infinite geometric series:

Thanks earboth.

So what you are saying is,
if I have a pie and cut it into three pieces and ate one of them, I would have two one-third pieces left. Then if I cut each of those one-third pieces into three pieces and ate one, I would have four one-ninth pieces. And if I continue cutting each piece into threes and eating one of them, I will eventually eat the entire pie.
Right?????

Originally Posted by shadow1

Thanks earboth.

So what you are saying is,
if I have a pie and cut it into three pieces and ate one of them, I would have two one-third pieces left. Then if I cut each of those one-third pieces into three pieces and ate one, I would have four one-ninth pieces. And if I continue cutting each piece into threes and eating one of them, I will eventually eat the entire pie.
Right?????

Hello,

that's it.

I would recommend this method as a diet because you eat an infinite amount of pieces in an endless time and finally and actually you ate only one pizza