Skip to content

Course home

1.7 D: Sequences and series

1.7 D: Sequences and series

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245
Question 225
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

1.7 D: Sequences and series Questions

  1. A Level
  2. /Maths
  3. /1.7 D: Sequences and series

308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank