Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2014 / Paper 1 / 19 / c / ii / Solution

Use the bound $|\sin n|\le 1$:The comparison p-series has exponent $2>1$ and converges. Hence, by the comparison test for series, the original series is absolutely convergent. No alternating-sign or monotonicity assumption about $\sin n$ is needed.