1. Not finding help here? Sign up for a free 30min 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!

Calculate sums math problem

  1. Dec 10, 2005 #1

    daniel_i_l

    User Avatar
    Gold Member

    I need to calculate
    [tex]
    \sum_{i=1}^n \frac{1}{i(i+1)}
    [/tex]
    useing the fact that:
    [tex]
    \sum_{i=1}^n F(i) - F(i-1) = F(n) - F(0)
    [/tex]
    now I chose the function
    [tex]
    F(i) = \frac{1}{i} \frac{1}{(i+1)} ... \frac{1}{(i+r)}
    [/tex]
    so
    [tex]
    F(i)-F(i-1)=(\frac{1}{i}\frac{1}{(i+1)} ... \frac{1}{(i+r-1)})(\frac{1}{(i+r)}-\frac{1}{(i-1)})
    [/tex]
    now I want to use that to calcualte the sum chooseing r as 2, but I'm stuck because the F(0) is undefined, and because of the
    [tex]
    \frac{1}{i+r}-\frac{1}{i-1})
    [/tex]
     
    Last edited: Dec 10, 2005
  2. jcsd
  3. Dec 10, 2005 #2

    shmoe

    User Avatar
    Science Advisor
    Homework Helper

    You need to choose F(i) so that

    [tex]
    F(i)-F(i-1)=\frac{1}{i(i+1)}
    [/tex]

    Your choice of F(i) does not satisfy this (what is that r anyways?) Try another choice of F, with a hint-think partial fractions.
     
  4. Dec 10, 2005 #3

    Physics Monkey

    User Avatar
    Science Advisor
    Homework Helper

    Why on earth would you choose that three term nightmare for F? There is a much easier way to do it. Hint: what is [tex] \frac{1}{i+1} - \frac{1}{i} [/tex]?
     
  5. Dec 10, 2005 #4

    daniel_i_l

    User Avatar
    Gold Member

    Thanks a lot!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Calculate sums math problem
Loading...