1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Homework Helper


    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted