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∞(sin60∘)2n\sum_{n=1}^{\infty} (\sin 60^{\circ})^{2n}∑n=1∞(sin60∘)2n
Find the smallest positive exact value of θ\thetaθ, in radians, which satisfies the equation ∑n=0∞(tanθ)n=33−3\sum_{n=0}^{\infty} (\tan \theta)^n = \frac{3}{3 - \sqrt{3}}∑n=0∞(tanθ)n=3−33
Practise Edexcel A Level Maths 3.5 Sum to Infinity with exam-style questions for A Level Maths. 18 questions, 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.