Derive the following, for any integer k

[MRGSLSE]

I really need someone to answer this by tomorrow 12/01 10:50 am pacific time...

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

 

[MRGSLSE]

This one too please

4) Derive the following, for 0 < or equal x < or equal 2(pi)
infinity
Sum of: cos(nx)/n^2 = (3(x)^2-6(pi)(x)+2(pi)^2) / 12
n=1

 

[HallsofIvy]

This looks like homework to me.

(Especially when they are numbered "1." and "4."!)

 

[PrudensOptimus]

Can you at least make it more clear for us to even start? LOL? What are you talking about, sigma with top index infinity?

 

[MRGSLSE]

don't mind the index... its there, because it sets the infinity on top of the SUM OF: and sets the n=1 down below it... any clues...
there not homework... extra credit

 

[MRGSLSE]

thanks for not helping anyways, this assignment is done with...