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1.6 Sequences and Series

1.6 Sequences and Series

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Question 129

The calibration of a specialized velocity sensor C(v)C(v)C(v), where v v\,v represents a small change in velocity from a reference state, is modeled by the function:

C(v)=15(25+kv)−12 C(v) = 15(25 + kv)^{-\frac{1}{2}} C(v)=15(25+kv)−21​

Given that the binomial expansion of C(v)C(v)C(v) in ascending powers of v v\,v is P−0.12v+Rv2+…P - 0.12v + Rv^2 + \dotsP−0.12v+Rv2+…

a.

find the values of the constants kkk, PPP, and RRR.

[4]
b.

State the range of values of v v\,v for which this expansion is valid.

[1]
c.

For this expansion, find the coefficient of the term in v3v^3v3.

[2]
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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