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1.6 Sequences and Series

1.6 Sequences and Series

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Question 224
a.

Use the binomial expansion to expand

(9−4x)−12∣x∣<94 (9 - 4x)^{-\frac{1}{2}} \quad |x| < \frac{9}{4} (9−4x)−21​∣x∣<49​

in ascending powers of xxx, up to and including the term in x2x^2x2, giving each coefficient as a fully simplified fraction.

[4]
b.
f(x)=6+kx9−4xwhere k is a constant and ∣x∣<94 f(x) = \frac{6 + kx}{\sqrt{9 - 4x}} \quad \text{where } k \text{ is a constant and } |x| < \frac{9}{4} f(x)=9−4x​6+kx​where k is a constant and ∣x∣<49​

Given that the series expansion of f(x)f(x)f(x), in ascending powers of xxx, is

2+49x+px2+…where p is a constant 2 + \frac{4}{9}x + px^2 + \dots \quad \text{where } p \text{ is a constant} 2+94​x+px2+…where p is a constant

find the value of kkk,

[2]
c.

find the value of ppp.

[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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