comparison test

The series

$$\sum _{i=0}^{\mathrm{\infty }}{a}_i$$

with real $a_i$ is absolutely convergent if there is a sequence ${(b_n)}_{n\in \mathbb{N}}$ with positive real $b_n$ such that

$$\sum _{i=0}^{\mathrm{\infty }}{b}_i$$

is and for all sufficiently large $k$ holds $|a_k|\le b_k$.

Also, the series $\sum a_i$ is divergent if there is a sequence $(b_n)$ with positive real $b_n$, so that $\sum b_i$ is divergent and $a_k\ge b_k$ for all sufficiently large $k$.

Title	comparison test
Canonical name	ComparisonTest
Date of creation	2013-03-22 13:21:48
Last modified on	2013-03-22 13:21:48
Owner	mathwizard (128)
Last modified by	mathwizard (128)
Numerical id	4
Author	mathwizard (128)
Entry type	Theorem
Classification	msc 40A05