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1.4 Sequences and Series

1.4 Sequences and Series

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Question 234
a.

Find the first two terms, in ascending powers of uuu, of the binomial expansion of

(1+2u)13 (1 + 2u)^{\frac{1}{3}} (1+2u)31​
[2]
b.

Hence, for small values of xxx, show that

cos⁡3x+1−x23≈A+Bx+Cx2 \cos 3x + \sqrt[3]{1 - x^2} \approx A + Bx + Cx^2 cos3x+31−x2​≈A+Bx+Cx2

where AAA, BBB and CCC are constants to be found.

[5]
Markscheme

1.4 Sequences and Series Questions

  1. A Level
  2. /Maths
  3. /1.4 Sequences and Series

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.

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