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1.6 Sequences and Series

1.6 Sequences and Series

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Question 163
a.

The power output PPP, in kilowatts, of a prototype wind turbine is modeled by the function

P(v)=(2+v10)12 P(v) = \left(2 + \frac{v}{10}\right)^{12} P(v)=(2+10v​)12

where v≥0v \ge 0v≥0 is the wind speed in m/s. Find, in ascending powers of vvv, up to and including the term in v3v^3v3, the binomial expansion of P(v)P(v)P(v), fully simplifying each coefficient.

[4]
b.

Use the answer to part (a) to find an approximation for the power output when the wind speed is 0.50.50.5 m/s, which corresponds to evaluating 2.05122.05^{12}2.0512. Give your answer to 2 decimal places.

[2]
c.

Without calculating the exact value of 2.05122.05^{12}2.0512, state, with a reason, whether the answer to part (b) is an overestimate or an underestimate.

[1]
Markscheme

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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