Derive the following, for any integer k

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    Derive Integer
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Discussion Overview

The discussion revolves around deriving specific mathematical series for any integer k, focusing on two distinct summations involving series expansions and trigonometric functions. The context appears to be related to advanced mathematics, possibly within a homework or extra credit framework.

Discussion Character

  • Homework-related, Mathematical reasoning, Debate/contested

Main Points Raised

  • Post 1 presents a summation involving the series for 1/(n^(2k)) and relates it to Bernoulli numbers, seeking a derivation for any integer k.
  • Post 2 requests a derivation for a summation involving cos(nx)/n^2, providing a specific formula for the result.
  • Post 3 suggests that the requests may be homework-related due to the structured numbering of the problems.
  • Post 4 expresses confusion regarding the notation used, particularly the summation index and its limits.
  • Post 5 clarifies the notation, indicating that the index denotes the upper limit of the summation and attempts to downplay the homework implication by stating it is for extra credit.
  • Post 6 expresses frustration over the lack of assistance and indicates that the assignment is completed regardless of the discussion.

Areas of Agreement / Disagreement

Participants appear to disagree on whether the requests are homework-related, with some asserting it is while others contest this notion. The clarity of the mathematical notation also remains a point of contention.

Contextual Notes

There are unresolved aspects regarding the assumptions behind the derivations requested, particularly concerning the definitions of the series and the context of the problems presented.

MRGSLSE
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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:
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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
 
This looks like homework to me.

(Especially when they are numbered "1." and "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?
 
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
 
thanks for not helping anyways, this assignment is done with...
 

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