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1.6 Sequences and Series

1.6 Sequences and Series

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Question 222

A researcher models the intensity I I\,I of a signal as it penetrates a specific material of thickness x x\,x cm. The model is given by

I(x)=(1+23x)−3for ∣x∣<32 I(x) = \left(1 + \frac{2}{3}x\right)^{-3} \quad \text{for } |x| < \frac{3}{2} I(x)=(1+32​x)−3for ∣x∣<23​

Find the binomial expansion of I(x)I(x)I(x) in ascending powers of x x\,x up to and including the term in x3x^3x3. Simplify each coefficient fully and present them as exact fractions.

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1.6 Sequences and Series Questions

  1. A Level
  2. /Maths
  3. /1.6 Sequences and Series

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.

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