Vipul at 15:45, 26 July 2013

2013-07-26T15:45:02Z

← Older revision		Revision as of 15:45, 26 July 2013
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	Full timed transcript: <toggledisplay>		Full timed transcript: <toggledisplay>

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	Vipul: Okay, so this talk is going to be about		Vipul: Okay, so this talk is going to be about
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	Now the series is called conditionally convergent		Now the series is called conditionally convergent
	~~if it~~

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	with the degree difference test, which basically		with the degree difference test, which basically
	again follows from the integral test~~. This~~		again follows from the integral test, this

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	~~actual function~~ summation does not converge.		absolute value summation does not converge.
	You do have examples of series that are convergent		You do have examples of series that are convergent

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	So a_1 + a_2 + ... + a_{n-1} and the next		So a_1 + a_2 + ... + a_{n-1} and the next
	partial sum is a_1 + a_2 + ... + a_{n-1} ~~plus~~		partial sum is a_1 + a_2 + ... + a_{n-1} + a_n.

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	~~a_n.~~ You've added a_n,right? If this partial		You've added a_n,right? If this partial
	sum is in the ball, in this interval, and		sum is in the ball, in this interval, and

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	not absolutely convergent. Similarly, negative		not absolutely convergent. Similarly, if the
	terms		negative terms

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	converged, the positive terms ~~fall to~~ converge		converged, the positive terms also converge
	and then the absolute value will also have		and then the absolute value will also have

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	it's just this. It is the limit as n approaches		it's just this. It is the limit as n approaches
	~~inf~~. Inf just means... is the shorthand for		infinity. Inf just means... is the shorthand for

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Vipul: /* Statement */

2013-07-25T20:47:50Z

Statement

Show changes

Vipul: Created page with "{{perspectives}} The videos here are part of (though not the entirety of) the playlist: * [https://www.youtube.com/playlist?list=PLC0bHnWu122kRWwvivtI5hTNJx8J3GCbt&feature=v..."

2012-12-22T21:43:38Z

Created page with "{{perspectives}} The videos here are part of (though not the entirety of) the playlist: * [https://www.youtube.com/playlist?list=PLC0bHnWu122kRWwvivtI5hTNJx8J3GCbt&feature=v..."

New page

{{perspectives}}

The videos here are part of (though not the entirety of) the playlist:

* [https://www.youtube.com/playlist?list=PLC0bHnWu122kRWwvivtI5hTNJx8J3GCbt&feature=view_all Alternating series and Riemann series rearrangement theorems]

==Statement==

<center>{{#widget:YouTube|id=LFez_mErpjA}}</center>

==Related facts==

==Proof==

===Proof of (1), (2), and (3)===

(see video above)

===Proof of (4)===

<center>{{#widget:YouTube|id=y5fHRkgsZpo}}</center>

Video:Riemann series rearrangement theorem - Revision history

Vipul at 15:45, 26 July 2013

Vipul: /* Statement */

Vipul: Created page with "{{perspectives}} The videos here are part of (though not the entirety of) the playlist: * [https://www.youtube.com/playlist?list=PLC0bHnWu122kRWwvivtI5hTNJx8J3GCbt&feature=v..."