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!

Trying to solve this infinite series?

  1. Oct 11, 2013 #1
    Trying to solve this infinite series??

    Hey folks! I've spent hours trying to solve this and have exhausted all available resources.. I just need to be pointed in the right direction!

    1. The problem statement, all variables and given/known data
    Compute the sum of the infinite series (I believe this is an arithmetico geometric series):
    [itex]\sum \frac{n+1}{4^{n}}[/itex]

    For n=0..infinity

    2. Relevant equations
    I know the standard way to solve a geometric series, but don't know how to solve this type of series.


    3. The attempt at a solution
    I've set up something like this:
    [itex]S_{n} = \sum \frac{n+1}{4^{n}}[/itex]
    I've tried multiplying by 1/4, 4 and other logical things, but am just not sure how to proceed.

    Thanks in advance!!
     
  2. jcsd
  3. Oct 11, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Your expression can be written as
    $$\sum_0^\infty \frac{1}{4^{n}} + \sum_1^\infty \frac{1}{4^{n}} + \sum_2^\infty \frac{1}{4^{n}} + \dots$$
    (This assumes you start your sum at 0, if you start at 1 you have to modify it a bit.)
     
  4. Oct 12, 2013 #3

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Another approach, perhaps more general in application, is to multiply the terms by xn then integrate. You should then be able to sum the series into closed form and differentiate to get a closed form for the original sum. Finally set x=1.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Trying to solve this infinite series?
  1. Infinite series (Replies: 4)

  2. Infinite Series (Replies: 2)

  3. Infinite series. (Replies: 4)

  4. Infinite series. (Replies: 1)

Loading...