Convergence tests for series: Determine the convergence of the following series. Justify your answers with proofs.
(a) ∑(n²)/(2ⁿ)
(b) ∑(sin(n²))
a) Both series converge
b) Both series diverge
c) Series (a) converges, series (b) diverges
d) Series (a) diverges, series (b) converges