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=3−33
