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!

Determine the term containing (Binomial Theorom)

  1. Dec 17, 2012 #1
    Determine the term containing.... (Binomial Theorom)

    1. The problem statement, all variables and given/known data

    Determine the term containing x^11 in the expansion (X^2 - 1/x)^10

    2. Relevant equations

    T(k+1) = nC(k)*A^(n-k)*b^K


    3. The attempt at a solution

    x^11 = 10Ck * (x^2)^(10-k)*(-X^-1)^k (taking out the (-) from the x^-1 b/c it dont matter)

    x^11 = 10ck *X^(20-2k)(X^-k)
    x^11/(X^20-3k) = 10ck
    x^3k-9 = 10ck

    Im stuck here.
     
    Last edited: Dec 17, 2012
  2. jcsd
  3. Dec 17, 2012 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Re: Determine the term containing.... (Binomial Theorom)

    Start by finding the coefficient of x1. That should give you a hint.
     
  4. Dec 17, 2012 #3
    Re: Determine the term containing.... (Binomial Theorom)

    Its just 1. How does that help me ?
     
  5. Dec 17, 2012 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Determine the term containing.... (Binomial Theorom)

    I don't think it is 1. [itex](x^2-\frac{1}{10})^{10}[/itex] contains only even powers of x, doesn't it? Forget the binomial theorem and just imagine what would happen if you start expanding it by hand.
     
  6. Dec 17, 2012 #5
    Re: Determine the term containing.... (Binomial Theorom)




    Mistake in my question.
     
  7. Dec 17, 2012 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Determine the term containing.... (Binomial Theorom)

    Yeah. So you want [itex](x^2-\frac{1}{x})^{10}[/itex]. Factor out the x^2. So now you've got [itex]x^{20} (1-\frac{1}{x^3})^{10}[/itex]. What power do you want in the second factor?
     
  8. Dec 17, 2012 #7
    Re: Determine the term containing.... (Binomial Theorom)

    Woah how did you get that? And im looking for the term with X^11.
     
  9. Dec 18, 2012 #8

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Determine the term containing.... (Binomial Theorom)

    I used algebra. And to go back to your first post, which was pretty hard to read especially with the wrong problem statement, you want 20-3k=11. What's k? And the sign does matter.
     
  10. Dec 18, 2012 #9
    Re: Determine the term containing.... (Binomial Theorom)

    Ok, so I'm looking for the term containing X^11. I tried using the formula T(k+1) = nC(k)*A^(n-k)*b^K. K is the variable of the formula.
     
  11. Dec 18, 2012 #10
    Re: Determine the term containing.... (Binomial Theorom)

    n is 10.
     
  12. Dec 18, 2012 #11
    Re: Determine the term containing.... (Binomial Theorom)

    I know the answer is 4 b/c it would be. 10c3(x^2)^7(-1/x)^3. However I dont care what the constant term is.
     
  13. Dec 18, 2012 #12
    Re: Determine the term containing.... (Binomial Theorom)

    K is 3 making the term 4 according to the formula T(k+1) = nC(k)*A^(n-k)*b^K.
     
  14. Dec 18, 2012 #13

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Determine the term containing.... (Binomial Theorom)

    You were almost there is the first post. You want the exponent in (x^2)^(10-k)*(x^(-k)) to be 11. What's k?
     
  15. Dec 18, 2012 #14

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Determine the term containing.... (Binomial Theorom)

    Yes, k=3. Now think a little about the sign of the coefficient.
     
  16. Dec 18, 2012 #15
    Re: Determine the term containing.... (Binomial Theorom)

    Yes its negative, however cant I just dismiss the coefficient since i'm only looking for its variable ?
     
  17. Dec 18, 2012 #16

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Re: Determine the term containing.... (Binomial Theorom)

    Dick took a factor of x2 out of each of the 10 brackets. That turned each bracket into 1-1/x3, and combining the 10 factors outside produced x20.
    Now imagine expanding the (1-1/x3)10. Suppose some term of that has the x power as 1/xk. You want the one which, when multiplied by x20, produces x11.
     
  18. Dec 18, 2012 #17

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Determine the term containing.... (Binomial Theorom)

    You threw away the sign and got 10C3 once you figured out k=3. But you shouldn't have thrown away the sign. It might be -10C3.
     
  19. Dec 18, 2012 #18
    Re: Determine the term containing.... (Binomial Theorom)

    I like how this was solved with mental thinking. But how would you solve it using sheer algebra ?
     
  20. Dec 18, 2012 #19
    Re: Determine the term containing.... (Binomial Theorom)

    You know, what you guys showed / helped me with is enough to solve similar questions. Thank you. I didnt know you can take x^2 out of (x^2 - 1/x)^10
     
  21. Dec 18, 2012 #20

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Determine the term containing.... (Binomial Theorom)

    You very nearly already did it in the first post. Add the insight that k must be 3, don't ignore the sign and try to write it out in a coherent way.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Determine the term containing (Binomial Theorom)
  1. Binomial expansion (Replies: 14)

  2. Binomial expansion (Replies: 2)

Loading...