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Math Help - counting query

  1. #1
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    counting query

    Can anyone help me find the sixth term of \left( x - \frac{1}{2}\right)^{10} ?

    Thanks.
    Last edited by mr fantastic; April 24th 2009 at 07:25 AM. Reason: Clarified the equation by re-formatting in Latex
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  2. #2
    MHF Contributor
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    Quote Originally Posted by 14041471 View Post
    Find the sixth term of (x )10
    A quick way (and probably the simplest way) is to apply the Binomial Theorem. To find the m-th term of a binomial with first term "a", second term "b", and power "n", use:

    . . . . . \frac{n!}{m!(n\, -\, m)!}\, a^{n-m} b^{m}

    Note: Remember to count the first term as "m = 0", so "the sixth term" is really "m = 5".

    . . . . . \frac{10!}{5!(10\, -\, 5)!}\,\left( x^{10-5} \right) \left(-\frac{1}{2}\right)^{5}
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