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maths-binomial theorem

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how can we show that there is no constant
in the expansion of [2x – (x^2/4)]^9

  • maths-binomial theorem -

    general term
    = C(9,n) (2x)^(9-n) (x^2/4)^n
    = C(9,n) 2^(9-n) x^(9-n) (1/4)^n x^2n)
    = C(9,n) (2^(9-n)(1/4)^n x^(9+n)

    to have a constant, the exponent of x^(9+n) must be zero
    so 9+n = 0
    n = -9
    BUT, n must be a positive integer, so there is no constant term in the expansion.

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