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.