# Lobachevskii criterion (for convergence)

From Encyclopedia of Mathematics

A series with positive terms tending monotonically to zero converges or diverges according as the series

converges or diverges, where is the largest of the indices of the terms that satisfy the inequality , .

It was proposed by N.I. Lobachevskii in 1834–1836.

**How to Cite This Entry:**

Lobachevskii criterion (for convergence).

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Lobachevskii_criterion_(for_convergence)&oldid=17486

This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article