Comparison test
Comparison test can mean:
- Limit comparison test, a method of testing for the convergence of an infinite series.
- Direct comparison test, a way of deducing the convergence or divergence of an infinite series or an improper integral.
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Suppose that 0<a_n\leq b_n for each n\in\mathbb{N}. Then we have:
(i) If \sum_{n=1}^\infty b_n$ converges, then \sum_{n=1}^\infty a_n converges.
(ii) If \sum_{n=1}^\infty a_n diverges, then \sum_{n=1}^\infty b_n diverges.