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!

Trying to prove this equality involving a summation of a binomial coefficient.

  1. Oct 13, 2012 #1
    I immediately thought of induction, so that is what I used, but I can't seem to make any progress past a certain point.

    1-1.png

    2-1.png
     
  2. jcsd
  3. Oct 13, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi jdinatale! :smile:

    (i haven't looked at your induction proof , but …)

    why not just multiply the LHS by n+1 ? :wink:
     
  4. Oct 14, 2012 #3
    Ok, I tried that and I eventually could not go any further. Any ideas on what's going wrong?

    3-1.png
     
  5. Oct 14, 2012 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi jdinatale! :smile:

    in the third line you have ∑k=0…j j+1Ck+1

    put m = k+1, that's ∑m=1…j+1 j+1Cm

    what is that? :wink:
     
  6. Oct 14, 2012 #5
    Brilliant! I've solved the problem now, thank you so much. But please tell me, how did you possibly know to do that? That was not obvious to me at all, and I'm not sure how you would just know to do that.
     
  7. Oct 15, 2012 #6

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    easy! :smile:

    the clue was in the question …

    the RHS said 2n+1,

    which i know is ∑ n+1Cr :wink:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Trying to prove this equality involving a summation of a binomial coefficient.
Loading...