2.2: Binomial expansion and numerical approximation

0606/21/M/J/17 — Question 5 · 5 marks · Binomial

Given that

a

is a constant.

(i)

Expand

(2 + ax)^{4}

, in ascending powers of

x

, simplifying each term of your expansion.

[2]

(ii)

Given also that the coefficient of

x^{2}

is equal to the coefficient of

x^{3}

, show that

a = 3

[1]

(iii)

Use your expansion to show that the value of

1.97^{4}

is 15.1 to 1 decimal place.

[2]