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Homework Help: Summing an infinite series question!

  1. Apr 23, 2013 #1
    1. The problem statement, all variables and given/known data

    I need to fin the sum of the following two infinite series:
    1. Ʃ[n=0 to ∞] ((2^n + 3^n)/6^n)

    and 2. Ʃ[n=2 to ∞] (2^n + (3^n / n^2)) (1/3^n)




    2. Relevant equations

    use the sum Ʃ[n=2 to ∞] (1/n^2) = ∏^2 / 6 as necessary



    3. The attempt at a solution

    I tried to manipulate them both to make them geometric or telescoping, to no avail. It seems like neither series is telescoping or geometric, so isn't it impossible to definitively sum them?

    I started to sum them by adding their partial sums, but they converge very slowly and it would take hundreds of calculations to provide enough evidence for the sums.
     
  2. jcsd
  3. Apr 23, 2013 #2

    Curious3141

    User Avatar
    Homework Helper

    Hint:

    1. Split them into two rational expressions. Simplify (ask what is ##\frac{a^n}{b^n}##?)

    2. Multiply the bracket out. Simplify.

    It's all just algebra.
     
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