Limit comparison test - Revision history

Vipul at 00:01, 29 April 2014

2014-04-29T00:01:18Z

← Older revision		Revision as of 00:01, 29 April 2014
Line 1:		Line 1:
	{{~~series~~ convergence test}}		{{convergence test}}

	==Statement==		==Statement==

Vipul: /* Statement */

2011-09-07T20:23:06Z

Statement

← Older revision		Revision as of 20:23, 7 September 2011
Line 13:		Line 13:
	Suppose, further, that the limit		Suppose, further, that the limit

	<math>\lim_{k \to \infty} frac{a_k}{b_k}</math>		<math>\lim_{k \to \infty} \frac{a_k}{b_k}</math>

	exists and is a nonzero real number. Then, the series <math>\sum_{k=1}^\infty a_k</math> is a convergent series if and only if the series <math>\sum_{k=1}^\infty b_k</math> is a convergent series.		exists and is a nonzero real number. Then, the series <math>\sum_{k=1}^\infty a_k</math> is a convergent series if and only if the series <math>\sum_{k=1}^\infty b_k</math> is a convergent series.

Vipul: Created page with "{{series convergence test}} ==Statement== Suppose we have two series of (eventually) positive terms: $\! \sum_{k=1}^\infty a_k$ and $\! \sum_{k=1}^\infty..."$

2011-09-07T20:22:29Z

Created page with "{{series convergence test}} ==Statement== Suppose we have two series of (eventually) positive terms: <math>\! \sum_{k=1}^\infty a_k</math> and <math>\! \sum_{k=1}^\infty..."

New page

{{series convergence test}}

==Statement==

Suppose we have two [[series]] of (eventually) positive terms:

<math>\! \sum_{k=1}^\infty a_k</math>

and

<math>\! \sum_{k=1}^\infty b_k</math>

Suppose, further, that the limit

<math>\lim_{k \to \infty} frac{a_k}{b_k}</math>

exists and is a nonzero real number. Then, the series <math>\sum_{k=1}^\infty a_k</math> is a convergent series if and only if the series <math>\sum_{k=1}^\infty b_k</math> is a convergent series.

==Related tests==

* [[Basic comparison test]]
* [[Degree difference test]]
* [[Root test]]
* [[Ratio test]]

Limit comparison test - Revision history

Vipul at 00:01, 29 April 2014

Vipul: /* Statement */

Vipul: Created page with "{{series convergence test}} ==Statement== Suppose we have two series of (eventually) positive terms: \! \sum_{k=1}^\infty a_k and \! \sum_{k=1}^\infty..."

Vipul: Created page with "{{series convergence test}} ==Statement== Suppose we have two series of (eventually) positive terms: $\! \sum_{k=1}^\infty a_k$ and $\! \sum_{k=1}^\infty..."$