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Finding the sum of an infinite series

  • Thread starter jspectral
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  • #1
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Homework Statement


[tex]\sum\frac{1}{n2^(n+1)}[/tex] from 1 to infinity.

By the way, that 2 is to the power of (n+1), doesn't show clearly.

Homework Equations


The Attempt at a Solution


I have worked out the first few individual calculations, up to n=6, and i know it approaches ln(2)/2, however I have no idea how to actually prove this.
 

Answers and Replies

  • #2
jbunniii
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What sorts of theorems do you know about power series?
 
  • #3
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What sorts of theorems do you know about power series?
A few, it's for a 2nd year university subject. We've been using proof by induction a fair bit, but other than that I don't know the actual names for them.
 
  • #4
What do you know of integrating power series?
 
  • #5
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What do you know of integrating power series?
You mean int(1 + x + x^2 + x^3 + ...) = x + x^2/2 + x^3/3 + ... ?
 
  • #6
jbunniii
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You mean int(1 + x + x^2 + x^3 + ...) = x + x^2/2 + x^3/3 + ... ?
Yes. See if you can work out how to apply that property to your problem.

(Hint: start by replacing the "1/2" with a variable.)

By the way, you can click on the following equation if you want to see how to typeset the sum properly:

[tex]\sum_{n=1}^{\infty}\frac{1}{n 2^{n+1}}[/tex]
 
Last edited:

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