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

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Homework Help Overview

The discussion revolves around the sum of a geometric series, specifically with an initial value of V_{0} = -1 and a common ratio of q = 1/3. Participants are examining the implications of the series and the formula for its sum.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • One participant attempts to calculate the sum of the series and presents a formula, while another questions the definition of Un, indicating a need for clarity on assumptions made in the problem.

Discussion Status

The discussion includes attempts to derive the sum of the series, with one participant expressing confidence in their result. However, there is no explicit consensus on the correctness of the calculations, and the need for clarification on certain terms remains.

Contextual Notes

Participants are navigating potential assumptions about the series, particularly regarding the definition of Un, which has not been provided in the initial statements.

mtayab1994
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Homework Statement


I already counted [tex]V_{0}=-1[/tex]

and [tex]q=\frac{1}{3}[/tex]

given: [tex]V_{n}=1-\frac{2}{U_{n}}[/tex]





Homework Equations



count: [tex]\sum_{k=0}^{n}V_{k}[/tex]


The Attempt at a Solution




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

is that correct?
 
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What is Un ... don't make us make assumptions.
 
I got it anyway. It's


[tex]S=-\frac{3}{2}(1-(\frac{1}{3})^{n+1})[/tex]
 
Well done.
 

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