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: Series/binomial/multinomial theorum

  1. Sep 27, 2007 #1
    1. The problem statement, all variables and given/known data

    for any positive interget n determine

    a) SUM(from i=0 to n) of


    b) SUM (from i=0 to n) of


    2. Relevant equations

    3. The attempt at a solution

    a) well i didnt realyl know how to start. i found that with
    n=1 then it becomes 1+1
    n=2 .5+1+.5
    n=3 1/3! + .5 +.5 +1/3!
    n=4 1/4! +1/3! +.25 +1/3! +1/4!
    n=4 1/5! +1/4! +.083333 +.083333 +1/4! +1/5!

    so i guess what i need is how do i get the middle term?
    or am i going about it wrong?

    for b) i know the sum is always 0, because ichecked it on my calculator. but i don't know hwo to prive that
  2. jcsd
  3. Sep 27, 2007 #2


    User Avatar
    Science Advisor

    Do you know what the binomial expansion of (1+x)n is?
  4. Sep 27, 2007 #3
    i acctulay think i got it
    a) 2^n/n!
  5. Sep 28, 2007 #4


    User Avatar
    Science Advisor

    Yes. Do the binomial expansion of (1+x)n, and the set x=1 or -1 to get the two versions of your problem.
  6. Sep 28, 2007 #5
    so is the 2^n/n! right?
    i get the same answer doing that as i do doing it long form (calculator)

    (mind helping on my other post ? :P)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook