Can this be solved? The other part is split into another question.

(a) Prove that S(N) = 4 . sin(2" ) and Sy converges 7. The convergence of S(N) to 7 is somehow more important than the way to compute them. The ancient way to prove S(N)'s convergence, however, does not use the prop- erties of trigonometric functions. Instead, an important inequality coming from geometric observations, can also help us prove the convergence. (b) Prove the Liu Hui's inequality: for every N 2 3, S(2N)