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Derive the following, for any integer k

  1. Nov 30, 2003 #1
    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
     
    Last edited: Nov 30, 2003
  2. jcsd
  3. Nov 30, 2003 #2
    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
     
  4. Dec 1, 2003 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    This looks like homework to me.

    (Especially when they are numbered "1." and "4."!!)
     
  5. Dec 1, 2003 #4
    Can you at least make it more clear for us to even start? LOL? What are you talking about, sigma with top index infinity?
     
  6. Dec 1, 2003 #5
    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
     
  7. Dec 1, 2003 #6
    thanks for not helping anyways, this assignment is done with...
     
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