Expansion of (x-(3/x^2)^9

acc

May 2010
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In the expansion of (x-(3/x^2)^9 find the following:

a) the term containing x6

b) the constant term

This is my last question, I swear! :p
 

mr fantastic

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In the expansion of (x-(3/x^2)^9 find the following:

a) the term containing x6

b) the constant term

This is my last question, I swear! :p
The general term is \(\displaystyle {9 \choose r} x^{9 - r} \left( -\frac{3}{x^2}\right)^r = {9 \choose r} (-3)^r x^{9 - r} x^{-2r} = {9 \choose r} (-3)^r x^{9 - 3r}\).

a) You require the coefficient of the power of x corresponding to 9 - 3r = 6.

b) You require the coefficient of the power of x corresponding to 9 - 3r = 0.