1.4 Sequences and Series - The Binomial Theorem

In a study of fluid dynamics, the pressure $P$ within a vessel at a specific depth $h$ is modeled by the expression

4 + kh)^5

where $k$ is a positive constant. For small values of $h$ , the pressure can be approximated by the binomial expansion

Ch^2 + Dh^3 + \cdots

where $A, B, C$ and $D$ are constants.

Find the value of $A$ .

[1]

Given that $B = 2 D$ and $k > 0$ ,

Find:

(i) the value of $k$

(ii) the value of $C$

[6]

1.4 Sequences and Series - The Binomial Theorem Questions