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Binomial Theorem

  1. Apr 20, 2004 #1
    I get a number that is too big when I calculate the coefficient of x^25 in:

    (2x - (3/x^2))^58

    This is how I found the coefficient:

    Code (Text):

    Note that (58) = A combination value...
               k

    (58) * (2x)^(58-k) * (-3/x^2)^k
     k
    (58) * (2)^(58 - k) * (x)^(58 - k) * (-3)^k * (1/x^2)^k
     k
    (58) * (2)^(58 - k) * (-3)^k * (x)^(58 - k) * (x)^-2k
     k
    (58) * (2)^(58 - k) * (-3)^k * (x)^(58 - 3k)
     k

    58 - 3k = 25
    -3k = -33
    k = 11

    So:

    (58) * 2^47 * (-3)^11 * (x)^25
     11
     
    This comes out to be a gigantic number. So I am unsure whether it is anywhere close to being correct despite that I thought that I followed the steps correctly. : \
     
  2. jcsd
  3. Apr 20, 2004 #2
    Thats the right answer; -5676647367067636376814212874240
     
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