Sequences and Series

Introduction (I made a mistake with the notation in this video...after the sigma, the subscript on the sequence should be i, not n, so when I changed the n to infinity, I should have also changed the n in the expression to i.)
http://screencast.com/t/NGY2MjBjODMt

Introduction continued (this is a short video):http://screencast.com/t/ODIwMWNl

Section 11.1 video 1:http://screencast.com/t/MTQ5YmM2M

Section 11.1 video 2 (a short video):http://screencast.com/t/MTg0NmNiMDct

Section 11.2 video 1:http://screencast.com/t/NmQzMmY5M2

Section 11.2 video 2:http://screencast.com/t/N2FiYzhmZ

Section 11.2 video 3:http://screencast.com/t/NzZkYTk1ZGUt

Section 11.2 video 4 (a short video):http://screencast.com/t/OTUxOTdk

Section 11.2 video 5:http://screencast.com/t/MTlmYWI1

Section 11.2 video 6:http://screencast.com/t/YTI0NmUzYm

Section 11.3 video 1: (You should be watching this on Monday, so ignore my statement about having a good weekend.)http://screencast.com/t/NzFlMGExNzYt

Section 11.3 video2:http://screencast.com/t/YjkyM2E4

Section 11.3 video3: (Ignore my reference to Louie.)http://screencast.com/t/OTk5MDA0

Section 11.3 video4: (I say I am going to be absent on Tuesday, but that is not true this year. I also say I will give you a sheet on the convergent tests, which I gave to you today.)http://screencast.com/t/ODg1NTM2Ym

Section 11.3 video5:http://screencast.com/t/YzIxZGMyZD

Section 11.3 video6:http://screencast.com/t/eOn10x5zZ

Section 11.4 video1:http://screencast.com/t/ZDg5ZDAwY

Section 11.4 video2:http://screencast.com/t/NzdlZjdiNGEt

Section 11.4 video3: (this is a short one)http://screencast.com/t/MjU0OTRiZD

Section 11.4 video4:http://screencast.com/t/NzIyNGYyNWU

Section 11.4 video 5:http://screencast.com/t/OTc3OTNmYT

Section 11.5 video1:http://screencast.com/t/NmI5MDBkNj

Section 11.5 video 2:http://screencast.com/t/NzhkOGRl

Section 11.5 video3:http://screencast.com/t/NzljNmRmZj

Section 11.5 video4 (error estimation):http://screencast.com/t/YzQ2NDlm

Section 11.5 video5 (error estimation):http://screencast.com/t/NTc4MWQ2

Section 11.5 video6 (error estimation):http://screencast.com/t/OWVlYTZhZDI

Section 11.5 video7 (error estimation):http://screencast.com/t/ODhjYTI0N

Note: In these videos, when I refer to "positive terms," I mean making all the terms positive, ie. the absolute value of all of the terms.

Section 11.6 video1:http://screencast.com/t/MjA1NWY2YmY

Section 11.6 video2:http://screencast.com/t/MmZhYmY3

Section 11.6 video3:http://screencast.com/t/NmEzNDA0

Section 11.6 video4:http://screencast.com/t/NjE0Yjk3OTE

Section 11.6 video5:http://screencast.com/t/NDczZTExZ

            Section 11.7 video1:http://screencast.com/t/N2I3NmIwY

Section 11.7 video2: (In this video, I make a mistake in eliminating a mult. choice option—I should have crossed out choice E instead of choice D…therefore, we cannot assum A is then answer until we show III diverges, which I will do in the next video.)http://screencast.com/t/OTI1ZDUyYTct

Section 11.7 video 3 (a short one):http://screencast.com/t/ZWZiMGIyMDE

Section 11.8 video1:http://screencast.com/t/MjI0YjUzYWU

Section 11.8 video2:http://screencast.com/t/ODVhMTIx

Section 11.8 video 3:http://screencast.com/t/ZTYwNjE5NWE

Section11.8 video4 (this video is less than 4 minutes):http://screencast.com/t/Yzg0ZjQ4OTMt

Section 11.8 video 5:http://screencast.com/t/ZTU3YTRh

Section 11.8 video6 (this is only 4 minutes):http://screencast.com/t/ZTkzNzE3Mjct

Section11.8 video7:http://screencast.com/t/MWMxZmYyNzYt

Section 11.8 video8 (with sound!):http://screencast.com/t/NmVjODJmZ

Section 11.8 video9 (with sound):http://screencast.com/t/YzRmMGY2ND

Section 11.9 video 1:http://screencast.com/t/NTAwNjEzM2

Section 11.9 video2 (It is a bit confusing at the end of this video...when I say it should be x^2, I am referring to the original problem #8 on p733. So I should have added the square to every step from the beginning, not just the last 2 steps) :http://screencast.com/t/YmJjNTUxN

Section 11.9 video3:http://screencast.com/t/YWU0ZTNhYmU

Section 11.9 video4 (this is example 7 on p731):http://screencast.com/t/NjBlNGIyMjA

Section 11.9 video5 (this includes example 6 on p731):http://screencast.com/t/MzkyOTMwZT

Section 11.9 video6:http://screencast.com/t/YjkwNzgyM2It

Section 11.10 video1:http://screencast.com/t/YjQ3MDlmZ

Section11.10 video2:http://screencast.com/t/MGIxMzRl

Section 11.10 video3:http://screencast.com/t/YjI4N2Y4N

Section 11.10 video4:http://screencast.com/t/NzU3NDQz

Section 11.10 video5:http://screencast.com/t/YTFhM2NiY2Q

Section11.10 video6:http://screencast.com/t/ZWFkNTBm

Section11.10 video7:http://screencast.com/t/YzMxMTgw

Section11.10 video8:http://screencast.com/t/NTRiYzYw

Section11.10 video9:http://screencast.com/t/MzEwYTAxMDg


Here is an example using the Lagrange Error Bound to estimate the accuracy of the 4th degree Taylor Polynomial of sinx centered at pi/6. (At the beginning of the video, I misspoke and said the n+1st derivative can be zero, but I meant to say that that the n+1st derivative could be negative, which is why it needs to be in absolute value.):
http://www.screencast.com/t/yNit8AAldr

Here we use the Lagange Error Bound to estimate sin38 degrees accurate to 5 decimal places. (Note at the end of the video, I said R3 was not accurate to 4 decimal places, but I meant to say that R3 was not accurate to desired 5 decimal places):
http://screencast.com/t/7q3PpxfTzt3

This example has some of the same ideas as the example above and it might help you to better understand the one above. It is an example of using an error bound (with an alternating series) to estimate a number to 4 decimal places. I misspoke a few times in this video, in the middle, I said we are putting in 1/2 for x, when I should have said -1/2. Towards the end, I said R5 equals, 0.000022, but I should have said B6, not R5, equals .000022.
http://screencast.com/t/gWrsrfDwnnw
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