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1.6 Sequences and Series

1.6 Sequences and Series

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Question 82

In a high-precision mechanical linkage system, the tolerance level T T\,T is modeled as a function of the misalignment factor δ \delta\,δ by the formula T(δ)=(4+cδ)5T(\delta) = (4 + c\delta)^5T(δ)=(4+cδ)5, where c c\,c is a constant. In a specific quality test, it is found that the coefficient of the δ2 \delta^2\,δ2 term in the binomial expansion of T(δ)T(\delta)T(δ) is 5760.

a.

Determine the possible values of ccc.

[3]
b.

The sensitivity S S\,S of the system is defined by the expression

S(δ)=(5512−14δ3)T(δ) S(\delta) = \left( \frac{5}{512} - \frac{1}{4\delta^3} \right) T(\delta) S(δ)=(5125​−4δ31​)T(δ)

Find the possible values of the term independent of δ \delta\,δ in the expansion of S(δ)S(\delta)S(δ).

[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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