A hydraulic system's pressure efficiency, E(h)E(h)E(h), at a depth hhh 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 hhh, of the binomial expansion of E(h)E(h)E(h), giving each coefficient in its simplest form.
By substituting h=0.01h = 0.01h=0.01 into your expansion from part (a), find an approximation for 15\sqrt{15}15.
Give your answer in the form ab\frac{a}{b}ba where aaa and bbb are integers to be found.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
