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Math Help - Binomial expression help!

  1. #1
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    Binomial expression help!

    Find the first three terms in these expansions in ascending powers of x
    a) (x+1/x)^6

    b) In the expansion of (1+x/2)^n in ascending powers of x the coefficent of x^2 is 30. Find n.

    Thanks in advance if you can help
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Confuzzled?
    Find the first three terms in these expansions in ascending powers of x
    a) (x+1/x)^6
    (x+1/x)^6=(1/x)^6+6(1/x)^5x+\frac{6\times 5}{2}(1/x)^4 x^2+...

    (x+1/x)^6=x^{-6}+6x^{-4}+15x^{-2}+...

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Confuzzled?
    b) In the expansion of (1+x/2)^n in ascending powers of x the coefficent of x^2 is 30. Find n.
    (1+x/2)^n =1+n(x/2)+\frac{n(n-1)}{2}(x/2)^2+...

    So the coeff of x^2 in the expansion is:

     \frac{n(n-1)}{8}=30,

    which has solutions n=-15 or n=16.

    I presume there is an implicit assumption that n \ge 1 so
    the answer would be n=16.

    RonL
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  4. #4
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    Thank you so much!
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