Series Structured Questions | Cambridge O Level Additional Mathematics

Question 1 of 5 · 10 marks

Series · 1 & 12.2 - Binomial Super Question

3 parts

Additional Mathematics 4037 · Question 1Paper 2 · Calculator[10 marks]

In the expansion of $(1 + ax)^n$ , where $n$ is a positive integer and $a

eq 0, the first three terms in ascending powers ofx $are$ 1 + 18x + 135x^2 + \dots$

(a)

Show that $n = 6$ and find the value of $a$ .

[4]

(b)

Hence, find the coefficient of $x^2$ in the expansion of $(2 - 3x)(1 + 3x)^6$ .

[3]

(c)

Find the term independent of $x$ in the expansion of $(1 + 3x)^6 \left(1 - \frac{2}{x}\right)^2$ .

[3]