Find the first four terms, in ascending powers of xxx, of the binomial expansion of
(3−13x)5 \left(3 - \frac{1}{3}x\right)^5 (3−31x)5Given that xxx is small, so terms in x4x^4x4 and higher powers of xxx may be ignored, show
(3−13x)5+(3+13x)5=a+bx2 \left(3 - \frac{1}{3}x\right)^5 + \left(3 + \frac{1}{3}x\right)^5 = a + bx^2 (3−31x)5+(3+31x)5=a+bx2where aaa and bbb are constants to be found.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
