# Sum of a geometric series

1. Dec 14, 2011

### mtayab1994

1. The problem statement, all variables and given/known data
I already counted $$V_{0}=-1$$

and $$q=\frac{1}{3}$$

given: $$V_{n}=1-\frac{2}{U_{n}}$$

2. Relevant equations

count: $$\sum_{k=0}^{n}V_{k}$$

3. The attempt at a solution

i counted the sum and i got : $$((\frac{1}{3})^{n+1}-1)(\frac{2}{3})$$

is that correct?

2. Dec 14, 2011

### Simon Bridge

What is Un ... don't make us make assumptions.

3. Dec 15, 2011

### mtayab1994

I got it anyway. It's

$$S=-\frac{3}{2}(1-(\frac{1}{3})^{n+1})$$

4. Dec 15, 2011

Well done.