This equation comes out of deriving the canonical partition function for some system. However, the question is more math based. I am having trouble understanding the simplification that was performed in the text:(adsbygoogle = window.adsbygoogle || []).push({});

∑ from N=0 to M of: (M!exp((M-2N)a))/(N!(M-N)!) supposedly becomes

exp(Ma)(1+exp(-2a))^M.... I tried to look at the first few terms and see how I can simplify this, and no dice... Anyone have any ideas? a is just a constant.

Also, the next step is that the above becomes (2cosh(a))^M Which is great, except, huh? I'm more of a scientist than a math person, so I apologize if I am missing something elementary.

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Statistics summation question:

**Physics Forums | Science Articles, Homework Help, Discussion**