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: Sum of coeff.

  1. Mar 19, 2007 #1
    1. The problem statement, all variables and given/known data


    [tex]^{30}C_0 ^{30}C_{10}-^{30}C1 ^{30}C_11+...+^{30}C_{20} ^{30}C_{30}[/tex]

    Again, I know this is some coeff of the product of some series, but I dont know how to find the series or the coeff.

    I dont know how to go about it.
  2. jcsd
  3. Mar 19, 2007 #2


    User Avatar
    Homework Helper
    Gold Member

    Is this the whole question?

    To evaluate it, wouldn't you actually need to know what the [itex]C_i[/itex] actually are?

    Because if they're unknown constants, then I have no idea what is meant by evaluating that. Plus, your equation is not totally clear. You have a negative randomly put it where all the others are positives. You should explicitly write when the negatives are to be.
  4. Mar 19, 2007 #3


    User Avatar
    Science Advisor

    Would those be the binomial coefficients? If so your nCi is more commonly written nCi.
  5. Mar 19, 2007 #4
    is the thing alternating or what?
  6. Mar 20, 2007 #5
    I'm assuming the thing is alternating..

    Try working out the first few terms...
    Alternately, try to write a formula for the nth term, and a formula for the (n+1)th term. See what happens when you add them together.
  7. Mar 20, 2007 #6
    Yes, those are binomial coefficients. The general term comes out to be

    [tex](-1)^n^{30}C_r ^{30}C_{10+r}[/tex] where r varies from 0 to 20.
  8. Mar 20, 2007 #7


    2. look at

    in general, when you have two series
    [tex]S_1=\sum_n a_n x^n[/tex]
    [tex]S_2=\sum_n b_n x^n[/tex]

    [tex]S_1S_2=\sum_n\sum_{i+j=n} a_i b_jx^n[/tex]
    Last edited: Mar 20, 2007
  9. Mar 21, 2007 #8
    Can someone work the first two steps or something and I can try to work the rest out?
  10. Mar 23, 2007 #9
    reformulate the problem, basically you are asked to find,

    [tex]\sum_{i=0}^{20} (-1)^n\binom{30}{i}\binom{30}{20-i}[/tex]

    look at the function
    [tex]f(x)=\sum_{n}\left [\sum_{i=0}^{20} (-1)^n\binom{30}{i}\binom{30}{20-i}\right ]x^n[/tex]

    from the equation I posted last time

    what can you conclude?
    what [itex]S_1[/itex] and [itex]S_2[/itex]
    should you construct to finish the problem?
    Last edited: Mar 23, 2007
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook