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Infinite series

  1. Apr 19, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the sum of the following series.

    SUM (n=1 to inf) -3^(n-1)/(8^n)

    2. Relevant equations

    Possibly fit into ar^n format?

    3. The attempt at a solution[/b

    I feel there is a way that this fits into a geometric form in which case could use a/(1-r) to find the infinite sum. I'm having trouble manipulating to fit into ar^n format when there are a couple powers of n in the general form.
    Can the scalar 'a' value have an exponent in it? I guess not then it would be an exponential not a scalar
  2. jcsd
  3. Apr 19, 2010 #2
    Your notation is ambiguous: do you mean [tex]\sum_{n=1}^\infty -\frac{3^{n-1}}{8^n}[/tex] or [tex]\sum_{n=1}^\infty \frac{(-3)^{n-1}}{8^n}[/tex] ?

    Either way, you should try to find a way to split this fraction into [tex]\left(\frac{a}{b}\right) \cdot \left(\frac{c}{d}\right)^n[/tex]. Then you will be able to apply the formula for the sum of a geometric series. You have the right idea; you just need to get the manipulations right.
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