Consider the expansion of

MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series

Problem

(5x^{2}+3/x)^{7}

. (i) Write the general term

T_{r+1}

of the expansion in terms of

r

. (ii) Show that the power of

x

occurring in

T_{r+1}

can be expressed as

14-3r

. Explain, in not more than two sentences, why the power depends linearly on

r

. (iii) Determine the value of

r

for which the term is independent of

x

(that is, contains

x^{0}

). Hence write that constant term of the expansion.