Binomially expand function of x/e

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SUMMARY

The discussion focuses on the binomial expansion of the function (1 - e^(-x))^(-1) using the binomial theorem. Participants confirm that the series expansion results in 1 + e^(-x) + e^(-2x) + ..., valid under the constraint that x > 0, ensuring that e^(-x) remains less than 1. This constraint is crucial for the convergence of the series.

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  • Understanding of the binomial theorem
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  • Basic calculus skills
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Homework Statement


(1-e^(-x))^(-1)


Homework Equations


Binomial theorem


The Attempt at a Solution


1+e^(-x)+e^(-2x)...
 
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coverband said:

Homework Statement


(1-e^(-x))^(-1)


Homework Equations


Binomial theorem


The Attempt at a Solution


1+e^(-x)+e^(-2x)...

That looks right, but just add in the constraint that x>0, since e(-x)<1
 

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