Binomial Expansion

Given that $k$ is a constant and the binomial expansion of

\sqrt{1 + kx}, \quad |kx| < 1

in ascending powers of $x$ up to the term in $x^3$ is

\frac{1}{4}x + Ax^2 + Bx^3

(i) find the value of $k$ ,

(ii) find the value of the constant $A$ and the constant $B$ .

[5]

Use the expansion to find an approximate value to $1.2\sqrt{1.2}$ .

Show your working and give your answer to 6 decimal places.

[4]

Binomial Expansion Questions