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Homework Help: Infinite Series: Find Function

  1. Nov 25, 2005 #1
    Hello all!
    I have the following infinite series:

    [tex]\frac{10}{x}+\frac{10}{x^2}+\frac{10}{x^3}+\ldots[/tex]

    How would I find a function, f(x), of this series?

    I know the series converges for [tex]\vert x \vert > 1[/tex]

    I think the function is: [tex]f(x) = \frac{10}{x-1}[/tex]

    but I'm not sure how to get it.

    Thanks,
    Bailey
     
  2. jcsd
  3. Nov 25, 2005 #2
    why the x-1 in the denominator?
    maybe this


    [tex]f_{n}(x) = \frac{10}{x^n}[/tex]

    because

    [tex]\sum\frac{10}{x^n}[/tex]

    will be what you started with, but I may be worng and/or missing something though.
     
    Last edited: Nov 25, 2005
  4. Nov 25, 2005 #3

    Physics Monkey

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    Hint: factor out a 10/x and see if the remaining series looks familiar to you.
     
  5. Nov 25, 2005 #4
    Ugggh! I'm so blind sometimes...must be all the turkey I ate yesterday. I see the geometric series.

    Thanks, PM.

    Bailey
     
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