ratio test

Let $(a_n)$ be a sequence of real numbers. Then the series

$$\sum _{n=1}^{\mathrm{\infty }}{a}_n$$

converges absolutely if

and diverges if

$$\underset{n\to \mathrm{\infty }}{lim\; inf}\left|\frac{a_{n+1}}{a_n}\right|>1.$$

Title	ratio test
Canonical name	RatioTest
Date of creation	2013-03-22 12:24:14
Last modified on	2013-03-22 12:24:14
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	12
Author	Koro (127)
Entry type	Theorem
Classification	msc 26A06
Classification	msc 40A05
Synonym	quotient criterion