How can the sum of a geometric series be evaluated?

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    Convergence Series
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Homework Help Overview

The discussion revolves around evaluating the sum of an infinite geometric series, specifically the series \(\sum(-1)^{n-1}*(\frac{4^n}{7^n})\). Participants are exploring the properties of geometric series and how to apply them to this particular series.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the nature of the series and its geometric properties. There is an attempt to clarify the form of the series and how it relates to the standard formula for geometric series. Questions are raised about the implications of rewriting terms and how that aids in finding the sum.

Discussion Status

The discussion is ongoing, with participants providing hints and references to the geometric series formula. There is an exploration of different interpretations of the series, but no consensus has been reached regarding the evaluation method.

Contextual Notes

Some participants note the importance of rewriting the series in a specific form to apply the geometric series sum formula, while others question the relevance of certain transformations. The original poster expresses uncertainty about the steps needed to arrive at the known answer.

thenewbosco
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i have the following series from 1 to infinity:
\sum(-1)^{n-1}*(\frac{4^n}{7^n})
how can i evaluate the sum of this?
thanks
i know the answer is 4/11 but i do not know how to get this.
 
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Look closer; it's just a geometrical serie.

What you might have missed: (-1)^{n-1}=(-1)^{n+1}.
 
how does this fact help me find what the sum is equal to?
 
It's like quasar said you need to rewrite into the form

\sum_{n=0}^{\infty} ar^n = \frac{a}{1-r}

where

a \neq 0
 

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