Mathematics

Mathematics

Problem

Let

n

be a positive integer. The expression

(3x^{2}-\dfrac{2}{x})^{n}

is expanded in ascending powers of

x

. a. (i) Write the general term

T_{r+1}

of the expansion in terms of

n

and

r

. b. (ii) Show that the power of

x

in

T_{r+1}

is

2n-3r

. c. (iii) For

n=8

, determine all integral values of

r

for which the term is independent of

x

.

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