The first three terms, in ascending powers of xxx, of the binomial expansion of (16+5x)12(16 + 5x)^{\frac{1}{2}}(16+5x)21 are given by
(16+5x)12≈a+58x−25512x2 (16 + 5x)^{\frac{1}{2}} \approx a + \frac{5}{8}x - \frac{25}{512}x^2 (16+5x)21≈a+85x−51225x2where aaa is a constant.
State the range of values of xxx for which this expansion is valid.
Choose from the options below:
∣x∣<516∣x∣<165∣x∣<4∣x∣<1 |x| < \frac{5}{16} \quad |x| < \frac{16}{5} \quad |x| < 4 \quad |x| < 1 ∣x∣<165∣x∣<516∣x∣<4∣x∣<1Find the value of aaa.
Choose from the options below:
14816 1 \quad 4 \quad 8 \quad 16 14816Practise 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.
