A materials scientist models the longitudinal strain ϵ\epsilonϵ in a composite beam using the function ϵ(h)=(14−3h)12\epsilon(h) = \left(\frac{1}{4} - 3h\right)^{\frac{1}{2}}ϵ(h)=(41−3h)21, where hhh is the applied load factor and ∣h∣<112|h| < \frac{1}{12}∣h∣<121. Find the first 4 terms, in ascending powers of hhh, of the binomial expansion for ϵ(h)\epsilon(h)ϵ(h), giving each coefficient in its simplest form.
By substituting h=1100h = \frac{1}{100}h=1001 into the expansion found in (a), find an approximation for 22\sqrt{22}22.
Give your answer in the form ab\frac{a}{b}ba where aaa and bbb are integers to be found.
308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.