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1.6 Sequences and Series

1.6 Sequences and Series

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Question 102
a.

A structural stability index SSS of a micro-beam is modeled as a function of its lateral displacement vvv by the expression S(v)=(2−14v)6S(v) = \left(2 - \frac{1}{4}v\right)^6S(v)=(2−41​v)6. Find the first four terms of the binomial expansion of S(v)S(v)S(v) in ascending powers of vvv.

[3]
b.

In a symmetric calibration test, the total response is defined as R(v)=(2−14v)6+(2+14v)6R(v) = \left(2 - \frac{1}{4}v\right)^6 + \left(2 + \frac{1}{4}v\right)^6R(v)=(2−41​v)6+(2+41​v)6. Given that vvv is sufficiently small such that terms in v4v^4v4 and higher powers of vvv may be neglected, show that

R(v)=A+Bv2 R(v) = A + Bv^2 R(v)=A+Bv2

where AAA and BBB are integers to be determined.

[3]
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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