A geometric sequence has first term 1 and common ratio 0.75.
(i) Find the sum to infinity, S∞S_{\infty}S∞, of the sequence.
(ii) Hence, or otherwise, evaluate
∑n=1∞(cos30∘)2n \sum_{n=1}^{\infty} (\cos 30^{\circ})^{2n} n=1∑∞(cos30∘)2nFind the smallest positive exact value of θ\thetaθ, in radians, which satisfies the equation
∑n=0∞(2cosθ)n=22−2 \sum_{n=0}^{\infty} (\sqrt{2}\cos \theta)^n = \frac{2}{2 - \sqrt{2}} n=0∑∞(2cosθ)n=2−22Practise 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.
