Need help finding the sum of a sequence

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    Sequence Sum
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Discussion Overview

The discussion revolves around finding the sum of the sequence defined by 2*(n-1)*x^(2n). Participants explore various methods, including integration and differentiation, to derive the sum, while expressing uncertainty about their approaches.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in integrating the term x^(2n) and suspects errors in their integration approach.
  • Another participant suggests substituting k=2n to simplify the integration of x^(2n).
  • A third participant reiterates the formula for integrating x^n and applies it to x^(2n), providing a specific integral expression but questions its utility in finding the sum.
  • One participant requests guidance on how to find the sum of the sequence.
  • Another participant proposes differentiating the sum of x^(2n) or x^(2(n-1)) as a potential method to proceed.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best method to find the sum, and multiple approaches are suggested without agreement on their effectiveness.

Contextual Notes

Participants express uncertainty about the integration process and its relevance to summing the sequence, indicating potential limitations in their understanding of the mathematical steps involved.

hyper
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I have to sequence 2*(n-1)*x^(2n), I have tried integrating and then finding the sum and then derivating the sum, and I allmost get the right answer.

But I think I am integrating wrong since I really don't know of the integrate when I have ^(2n), and not only n.

please help
 
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When you integrate x2n Just write k=2n. Then integral of xk is xk+1/(k+1) = x2n+1/(2n+1)
 
You know, I presume, that the integral of xn is 1/(n+1) xn+1+ C where n can be any number. Well, 2n is just a number! The integral of x2n is 1/(2n+1) x2n+1+ C. So the integral of 2(n-1)x2n is 2((n-1)/(2n+1))x2n+1. But I don't think that will help you find the sum!
 
How should I find the sum then?
 
differentiate sum x^2n and see what you get. Or better yet, differentiate x^(2(n-1))
 

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