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Infinite sums/series

  • Thread starter muso07
  • Start date
  • #1
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Homework Statement


Figuring out an infinite sum question for the kid I tutor... it's late and my brain's not functioning well. I think I'm overcomplicating the question, but I can't figure it out.

The the sum of the following infinite series:
S = 1+3x+5x^2+...

Homework Equations



The Attempt at a Solution


I got that tn = [tex](2n-1)x^{n-1}[/tex]

Which means the sum is
[tex]\Sigma (2n-1)x^{n-1}=2\Sigma nx^{n-1} - \Sigma x^{n-1} = 2\Sigma nx^{n-1} - \frac{1}{1-x}[/tex]

And here is where I get stuck...
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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Hi muso07! :smile:

Hint (for ∑ nxn-1):

integrate. :wink:
 
  • #3
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Hm, the kid's in Year 11 so he hasn't done integration yet...

But when you integrate, you get x^n. Then [tex]lim_{(a\rightarrow\infty)} [x^{n}]^{a}_{1}= lim_{(a\rightarrow\infty)}x^{a}-x=-x[/tex]
This isn't right, though... I feel like such an idiot. :P
 
  • #4
tiny-tim
Science Advisor
Homework Helper
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(have a sigma: ∑ and an infinity: ∞ and try using the X2 and X2 tags just above the Reply box :wink:)

No, you want d/dx lima->∞ (∑xn) :smile:
 
  • #5
54
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You beat me to replying. Is the sum (1+x)/(1-x)^2?
 
Last edited:
  • #6
54
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Nevermind, I'm just going to tell him to believe me and it shall be great.

Thanks for all your help!
 

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