Convergence Tests
Decide whether an infinite sum settles down.
Concept
Two tests cover most cases
p-series: ∑ 1/n^p converges exactly when p > 1. The harmonic series (p = 1) famously diverges.
Divergence test: if the terms do not approach 0, the series cannot converge. It never proves convergence — only failure.
∑ 1/n^p converges ⟺ p > 1