A theoretical model for the refractive index μ\muμ of a specialized optical glass depends on the incident light wavelength λ\lambdaλ according to the relation
μ(λ)=(1625+25λ)−32 \mu(\lambda) = \left( \frac{16}{25} + \frac{2}{5}\lambda \right)^{-\frac{3}{2}} μ(λ)=(2516+52λ)−23Determine the range of values of λ\lambdaλ for which the binomial expansion of μ(λ)\mu(\lambda)μ(λ) in ascending powers of λ\lambdaλ is valid.
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.