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 (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.