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