What is the Sum of a Geometric Series with a Given Initial Value and Ratio?

[mtayab1994]

Homework Statement

I already counted $$V_{0}=-1$$

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

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

Homework Equations

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

The Attempt at a Solution

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

is that correct?

 

[Simon Bridge]

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

 

[mtayab1994]

I got it anyway. It's


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

 

[Simon Bridge]

Well done.