**Question Corner and Discussion Area**

I have been trying to find the sum of:This summation can be broken up and rewritten. Splitting the fraction into two pieces by writing as the sum of and , then rewriting as and simplifying, gives(where

nis a positive integer), but have not been able to find the process for evaluating this power series. Any and all information on this problem would be greatly appreciated.

(the first sum runs over all even integers *k*=2*q*, the second over
all odd integers *k*=2*q*+1, so the combined sum runs over all integers
*k*).

Now you should notice that the last summation is just the power series expansion of .

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