# Sum of infinite geometric series

1. Homework Statement

2. Homework Equations

3. The Attempt at a Solution

I don't get what I am doing wrong here, I have attached my solution below. The solution manual have their answer as 3e/(3-e). Thanks!

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Gib Z
Homework Helper
Try posting the question in LaTex from now on, attachments have to be approved and put extra load on the moderators.

I type really slow in Latex, I type faster in Mathtype in word, that's why I included as an attachment. Sorry. Anyhow, here is the link to that attachment

tiny-tim
Homework Helper
Hi motornoob101!

You got confused with your second ∑.

It should be e∑(e/3)^x-1, shouldn't it?

Erm I don't think get it.. So I have e^(x-1) which is same as (e^x) (e^-1) and e^-1 is (1/e) no?

HallsofIvy
$$\frac{e^n}{3^{n-1}}= \frac{1}{e}\left(\frac{e}{3}\right)^{n-1}$$
$$\frac{e^n}{3^{n-1}}= e\left(\frac{e}{3}\right)^{n-1}$$