Direct comparison test
In mathematics, the comparison test, sometimes called the direct comparison test to distinguish it from similar related tests (especially the limit comparison test), provides a way of deducing whether an infinite series or an improper integral converges or diverges by comparing the series or integral to one whose convergence properties are known. == For series == In calculus, the comparison test for series typically consists of a pair of statements about infinite series with non-negative (real-valued) terms: If the infinite series ∑ b n {\displaystyle \sum b_{n}} converges and 0 ≤ a n ≤ b n {\displaystyle 0\leq a_{n}\leq b_{n}} for all sufficiently large n (that is, for all n > N {\displaystyle n>N} for some fixed value N), then the infinite series ∑ a n {\displaystyle \sum a_{n}} also converges.