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∘)nFind 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=2−32308 exam-style questions on OCR (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.