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1) Derive the following, for any integer k.

infinity

SUM OF: 1/(n^(2k)) = ((2(pi))^(2k)(-1)^(k+1)B2k ) /(2(2k)!)

n=1

where Bn is defined by the following, for |x| < 2(pi).

````````````infinity

(x)/(e^(x)-1) = SUM OF: (Bn x^n) / (n!)

````````````n=0

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# Derive the following, for any integer k

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