Mathematics

Problem

Let

n

be a positive integer and

a,b

be non–zero real numbers. a. (i) For

(ax+\dfrac{b}{x})^{n}

, obtain an expression for the power of

x

occurring in the general term

T_{r+1}

in terms of

r

. b. (ii) Hence derive the condition that

r

must satisfy for

T_{r+1}

to be independent of

x

. c. (iii) Using the result of part (ii), find the independent term in

(5x-\dfrac{2}{x})^{10}