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: Combinations Problem

  1. May 20, 2008 #1
    1. The problem statement, all variables and given/known data
    http://img234.imageshack.us/img234/8519/combgf7.png [Broken]​
    [/URL]


    2. Relevant equations
    [tex]{t}_k_+_1=_n{C}_kx^n^-^ky^k[/tex]


    3. The attempt at a solution
    The picture I have shown contains the problem and the teacher's solution. However, I was wondering how the [tex]k[/tex] value is 3. And no, I can't ask the teacher; my test is tomorrow.
     
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. May 20, 2008 #2

    rock.freak667

    User Avatar
    Homework Helper

    This is how I would do it

    [tex](x^2+\frac{1}{x})^{10}=[\frac{1}{x}(x^3+
    1)]^{10}[/tex]

    [tex]=\frac{1}{x^{10}}(x^3+1)^{10}[/tex]

    and you want the coefficient of [itex]x^11[/itex]

    so if you expand you will get

    [tex]=\frac{1}{x^{10}}(...+^{10}C_k(1)^{10-k}(x^3)^k+...)[/tex]

    You need to find k and you want the power of x to be 11

    so that 3k-10=11

    See it?
     
  4. May 20, 2008 #3
    For your expansion, isn't the 1 supposed to be where the [tex]x^3[/tex] is? Because 1 is the y value, while [tex]x^3[/tex] is the x value.

    Also, k doesn't equal 3 in [tex]3k-10=11[/tex]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook