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∑ 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!