Posted by **anoynomous** on Friday, March 22, 2013 at 2:22pm.

how can we show that there is no constant

in the expansion of [2x – (x^2/4)]^9

- maths-binomial theorem -
**Reiny**, Friday, March 22, 2013 at 2:34pm
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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