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: Summation with binomial coefficients question

  1. Apr 29, 2015 #1
    1. The problem statement, all variables and given/known data
    ##\sum\limits_{r=0}^n\frac{1}{^nC_r}=a##. Then find the value of $$\sum\sum\limits_{0\le i<j\le n}(\frac{i}{^nC_i}+\frac{j}{^nC_j})$$

    2. Relevant equations

    I have used two equations which I derived myself. This is the first one.
    The second one is:

    3. The attempt at a solution

    Using first equation and second equation:
    Now I have to subtract the cases where I=j to get the required sum. But Iis the above conclusion correct? Because I am not getting the required answer after subtracting.

    Attached Files:

  2. jcsd
  3. Apr 29, 2015 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    In the last line of the derivation of your second equation, you have been inconsistent in your substitutions of m for n. Two m's should be m+1.
    But I don't understand how you use this equation anyway. a is a function of n, but where you use the equation you seem to be using it as a generic fact for any m, without changing a. I.e. you cannot now substitute n for m as being equal.
  4. Apr 30, 2015 #3
    Then how do you find ##(2n+1)\sum\limits_{r=0}^n\frac{r}{^nC_r}##?
  5. Apr 30, 2015 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I haven't solved it myself, yet.
    You could try concentrating on one of the two terms in the double sum. You should be able to sum that over the 'other' variable.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted