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Combinations Problem

  • Thread starter temaire
  • Start date
  • #1
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Homework Statement


http://img234.imageshack.us/img234/8519/combgf7.png [Broken]​
[/URL]


Homework Equations


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


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.
 
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Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
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?
 
  • #3
279
0
[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
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]
 

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