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I'm working through an example from class and the textbook, but I'm confused about how the steps progress mathematically.

The example involves the Gibb's partition for a paramagnet.

[tex] \sum_{s} exp(\beta \mu B \sum_{i}^{N} s) [/tex]

Where s = -a,-a+1...a for each spin.

Am I right in thinking the sum in the exponent is a sum over this particles in the sample (N). Since a sum in an exponent is a product of the exponentials we get:

[tex] [\sum_{s} exp(\beta \mu B s)]^{N} [/tex]

However, I'm not sure what do with the second sum. I can't see a neat way proceed. Can anyone point me in the right direction?

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# Homework Help: Statistical mechanics: Sums of exponentials with sums.

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