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=2−22178 exam-style questions on Edexcel A Level Maths Sequences and Series, covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series. Each one has a worked solution and a mark scheme showing where the marks go.