I'm having problems understanding how(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\frac{e^{-\hbar \omega / 2k_BT}}{1-e^{-\hbar \omega / k_BT}}

[/tex]

approximates to

[tex]

k_BT/ \hbar\omega

[/tex]

when

[tex]

T >> \hbar\omega/k_B

[/tex]

Seems like it should be simple but don't quite see how to arrive at this result.

*update*

I have tried using taylor expansions of [tex]exp(-x)[/tex] and [tex]1-exp(-x)[/tex] and just using the first expansion term since if [tex]T>>\hbar\omega/k_B[/tex] then [tex]\hbar\omega/k_BT[/tex] should be small. This seems to give the right answer but i'd be interested in knowing if indeed my method is ok and if there are alternate methods.

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# Approximation problem

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