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Homework Help: Convergence of series

  1. Oct 12, 2005 #1
    i have the following series from 1 to infinity:
    [tex]\sum(-1)^{n-1}*(\frac{4^n}{7^n})[/tex]
    how can i evaluate the sum of this?
    thanks
    i know the answer is 4/11 but i do not know how to get this.
     
  2. jcsd
  3. Oct 12, 2005 #2

    quasar987

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    Look closer; it's just a geometrical serie.

    What you might have missed: [itex](-1)^{n-1}=(-1)^{n+1}[/itex].
     
  4. Oct 12, 2005 #3
    how does this fact help me find what the sum is equal to?
     
  5. Oct 13, 2005 #4

    quasar987

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  6. Oct 13, 2005 #5

    Pyrrhus

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    It's like quasar said you need to rewrite into the form

    [tex] \sum_{n=0}^{\infty} ar^n = \frac{a}{1-r}[/tex]

    where

    [tex] a \neq 0 [/tex]
     
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