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=2−32
