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I'm getting this sum in the statistical mechanics for the rotating energy, any one can help with?

[tex]

Z_r = \sum\limits_{\ell = 0}^\infty {\left( {2\ell + 1} \right)e^{{\textstyle{{T_r } \over T}}\ell \left( {\ell + 1} \right)} }

[/tex]

If tex doesn't work here is it, Where the sum is from 0 to infinity

Z=Sum[(2L+1)exp(-x L(L+1))]

Seems simple lol !!

Thanks

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# How to take this sum?

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