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∘)2n
Find 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=2−22
Practise Edexcel A Level Maths Sequences and Series with exam-style questions for A Level Maths. 100 questions 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, matched to the Edexcel A Level Maths (9MA0) 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.