Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2021 / Paper 1 / 19 / a / iii

For every positive integer $n$, the bound $|\sin (\omega n)|\le 1$ givesFor $p<-1$, the positive p-series $\sum n^p$ converges. The comparison test therefore provesNo special arithmetic condition on $\omega$ is required for this sufficient condition.