3.85: Binomial expansion first four terms

0606/12/O/N/23 — Question 4 · 7 marks

(a)
It is given that the first four terms, in ascending powers of xx, in the expansion of (1x2)n\left(1-\dfrac{x}{2}\right)^{n} can be written in the form 18x+px2+qx31-8x+px^{2}+qx^{3}, where nn, pp and qq are integers. Find the values of nn, pp and qq.
[5]
(b)
Find the term independent of xx in the expansion of (2x2+x3)6\left(\dfrac{2}{x^{2}}+\dfrac{x}{3}\right)^{6}, giving your answer as a rational number.
[2]