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1.6 Sequences and Series

1.6 Sequences and Series

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Question 203

The structural load L(w)L(w)L(w) of a specific beam under stress is modeled by the function L(w)=(5+3w)(2+kw)4L(w) = (5 + 3w)(2 + kw)^4L(w)=(5+3w)(2+kw)4, where www represents the deflection in millimetres and kkk is a stiffness constant.

a.

Find the first three terms, in ascending powers of www, of the binomial expansion of

(2+kw)4 (2 + kw)^4 (2+kw)4

where kkk is a constant. Give each term in its simplest form.

[3]
b.

Given that in the expansion of L(w)L(w)L(w) the coefficient of w2w^2w2 is 24, determine the possible values of the stiffness constant kkk.

[4]
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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