1.4.1 Sequences and Series - The Binomial Theorem

A hydraulic system's pressure efficiency, $E (h)$ , at a depth $h$ meters is modeled by the function \

E(h) = \left(\frac{1}{4} - 10h\right)^{\frac{1}{2}} \quad |h| < 0.025{\char"24}$

Find the first 4 terms, in ascending powers of $h$ , of the binomial expansion of $E (h)$ , giving each coefficient in its simplest form.

[4]

By substituting $h = 0.01$ into your expansion from part (a), find an approximation for $15\sqrt{15}$ .

Give your answer in the form $ab\frac{a}{b}$ where $a$ and $b$ are integers to be found.

[3]

1.4.1 Sequences and Series - The Binomial Theorem Questions

A hydraulic system's pressure efficiency, $E (h)$ , at a depth $h$ meters is modeled by the function \

E(h) = \left(\frac{1}{4} - 10h\right)^{\frac{1}{2}} \quad |h| < 0.025{\char"24}$

Find the first 4 terms, in ascending powers of $h$ , of the binomial expansion of $E (h)$ , giving each coefficient in its simplest form.

[4]

By substituting $h = 0.01$ into your expansion from part (a), find an approximation for $15\sqrt{15}$ .

Give your answer in the form $ab\frac{a}{b}$ where $a$ and $b$ are integers to be found.

[3]