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Binomial Theorem problem

  1. Jul 31, 2013 #1
    I highlighted the portion in red in the paint document that I'm not understanding.

    How can we see by inspection that the product is equal to the series 2?
     

    Attached Files:

  2. jcsd
  3. Jul 31, 2013 #2

    pasmith

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    The term independent of x in the product is equal to the series (2); this is because the term independent of x is a sum of terms of the form [itex]kc_k x^k \times c_k/x^k = kc_k^2[/itex].
     
  4. Jul 31, 2013 #3

    The second line in the paint document is equal to n/xn(1 + (2n-1)x + (2n-1)(2n-1)/2!x2 + .....) by using the binomial theorem

    If we look at the coefficient of the second term it is equal to n(2n-1).

    If we compare the coeff. n(2n -1) with the coeff. of the second term of series (2) which is
    2c22 = 2(n-1)(n-2)/2! = n2 - 3n + 2 they are not equal.

    Hence n(2n-1) =/= n2 - 3n + 2
     

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  5. Jul 31, 2013 #4
    Never mind I see that u said its the sum of the terms.... I got it now
     
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