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: Finding the sum of the series

  1. May 9, 2012 #1
    So the question is find the sum of the series:


    [itex]\sum[/itex] from k = 1 to ∞ of 1 / k(k+3),

    now the solution they provided was:

    = 1/3 [ (1 - 1/4) + (1/2 - 1/5) + ...+ (1/n - 1/(n+3) ]

    =1/3 [ 1+ 1/2+1/3 -1/(n+1) - 1/(n+2) - 1/(n+3)]

    --> 11/18

    I'm stuck on how they were able to show the sum telescoping and why they were able to factor out the 1/3. Also how are you suppose to solve these sorts of questions?
     
  2. jcsd
  3. May 9, 2012 #2

    Mark44

    Staff: Mentor

    Rewrite 1/(k(k + 3)) as two fractions, using partial fraction decomposition.
     
  4. May 9, 2012 #3

    sharks

    User Avatar
    Gold Member

    [tex]\sum^{\infty}_{k=1} \frac{1}{k(k+3)}[/tex]
    First, express [itex]\frac{1}{k(k+3)}[/itex] as partial fractions.
     
  5. May 9, 2012 #4
    Darn. Have to go back and review that, but it makes sense to do that now, thanks.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook