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.)

Introduction continued (this is a short video):

Section 11.1 video 1:

Section 11.1 video 2 (a short video):

Section 11.2 video 1:

Section 11.2 video 2:

Section 11.2 video 3:

Section 11.2 video 4 (a short video):

Section 11.2 video 5:

Section 11.2 video 6:

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

Section 11.3 video2:

Section 11.3 video3: (Ignore my reference to Louie.)

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.)

Section 11.3 video5:

Section 11.3 video6:

Section 11.4 video1:

Section 11.4 video2:

Section 11.4 video3: (this is a short one)

Section 11.4 video4:

Section 11.4 video 5:

Section 11.5 video1:

Section 11.5 video 2:

Section 11.5 video3:

Section 11.5 video4 (error estimation):

Section 11.5 video5 (error estimation):

Section 11.5 video6 (error estimation):

Section 11.5 video7 (error estimation):

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:

Section 11.6 video2:

Section 11.6 video3:

Section 11.6 video4:

Section 11.6 video5:

            Section 11.7 video1:

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.)

Section 11.7 video 3 (a short one):

Section 11.8 video1:

Section 11.8 video2:

Section 11.8 video 3:

Section11.8 video4 (this video is less than 4 minutes):

Section 11.8 video 5:

Section 11.8 video6 (this is only 4 minutes):

Section11.8 video7:

Section 11.8 video8 (with sound!):

Section 11.8 video9 (with sound):

Section 11.9 video 1:

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) :

Section 11.9 video3:

Section 11.9 video4 (this is example 7 on p731):

Section 11.9 video5 (this includes example 6 on p731):

Section 11.9 video6:

Section 11.10 video1:

Section11.10 video2:

Section 11.10 video3:

Section 11.10 video4:

Section 11.10 video5:

Section11.10 video6:

Section11.10 video7:

Section11.10 video8:

Section11.10 video9:

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.):

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):

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.