A geometric sequence has first term 1 and common ratio 13\frac{1}{3}31.
Find the sum to infinity, S∞S_{\infty}S∞, of the sequence.
Hence, or otherwise, evaluate ∑n=1∞(tan30∘)n\sum_{n=1}^{\infty} (\tan 30^{\circ})^n∑n=1∞(tan30∘)n
Find the smallest positive exact value of θ\thetaθ, in radians, which satisfies the equation ∑n=0∞(sinθ)n=22−3\sum_{n=0}^{\infty} (\sin \theta)^n = \frac{2}{2 - \sqrt{3}}∑n=0∞(sinθ)n=2−32
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.