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1.6 Sequences and Series

1.6 Sequences and Series

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Question 94

The efficiency of a prototype thermal engine is modeled by the function E(h)=(5−2h)6E(h) = (5 - 2h)^6E(h)=(5−2h)6, where h h\,h represents a heat-loss coefficient.

a.

Find the first 4 terms, in ascending powers of hhh, of the binomial expansion of (5−2h)6(5 - 2h)^6(5−2h)6, giving each term in its simplest form.

[4]
b.

To determine the engine's performance under specific lab conditions, a researcher needs to estimate 4.9464.94^64.946. State the value of h h\,h that should be used in the expansion from part (a) to achieve this. (There is no need to carry out this calculation.)

[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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