Convergence of Infinite Series with Variable Terms?

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Homework Help Overview

The problem involves the convergence of an infinite series with variable terms, specifically the series defined by the sum from 0 to infinity of (2^n + 6^n)/(2^n6^n).

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses confusion and seeks guidance on how to approach the problem. Some participants suggest splitting the fraction into simpler components to facilitate analysis.

Discussion Status

Participants have provided hints regarding the manipulation of the series, indicating a productive direction for the original poster. However, there is no explicit consensus on the overall approach or solution yet.

Contextual Notes

The original poster indicates a lack of familiarity with relevant equations or methods, which may affect their ability to engage with the problem fully.

lmannoia
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Homework Statement


Sum from 0 to infinity of (2^n + 6^n)/(2^n6^n)


Homework Equations


No idea.


The Attempt at a Solution


I am completely dumbstruck on how to do this one. Could someone give me a hint on where to start? Thanks a lot!
 
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Try splitting the fraction into two pieces.
 
Try

\frac{2^n+6^n}{2^n 6^n}=\frac{1}{6^n}+\frac{1}{2^n}
 
Got it, thank you both very very much.
 

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