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∘)2nFind 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=3−33308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.