generalised binominal theorem question

**vserian** · August 16th 2009, 06:43 PM

when ( 1+2x) (1+Ax)^2/3 is expanded in asending powers of x the coefficient of the term n x is zero

1) find the values of A

2) when A has this value find the term in x^3 in the expansion of
( 1+2x) (1+Ax)^2/3 simplifly the coeeficient

**chisigma** · August 16th 2009, 09:19 PM

The binomial expansion of $(1+ax)^{\frac{2}{3}}$ is ...

$(1+ax)^{\frac{2}{3}}= \sum_{n=0}^{\infty} \binom{\frac{2}{3}}{n}\cdot (ax)^{n}= 1 + \frac{2}{3}\cdot a x -\frac{1}{9} (ax)^{2} + \frac{4}{81}\cdot (ax)^{3} - \dots$ (1)

At this point the research of the value of a is a pure algebraic practice ...

Kind regards

$\chi$ $\sigma$

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