Math 2B. Calculus. Lecture 20. Series

UCI Math 2B: Single-Variable Calculus (Fall 2013)
Lec 20. Single-Variable Calculus -- Series --
Instructor: Natalia L. Komarova Ph.D.

License: Creative Commons CC-BY-SA

Description: UCI Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: Definite integrals; the fundamental theorem of calculus. Applications of integration including finding areas and volumes. Techniques of integration. Infinite sequences and series. Parametric and polar equations.

Recorded on November 15, 2013

[fjso]

At 11:54, it took me a moment to realize where the division by (1-r) came from. In case it helps anyone else watching:

Sn-rSn = a-ar^n
Sn(1-r) = a(1-r^n)
Sn = [a(1-r^n)] / (1-r)

[Algebrainiac]

9:24 r is the ratio not the power. (n-1) is the power…

[AlbJoel]

The sum of the arithmetic progression is exactly the same than the triangular numbers in the context of the figurate numbers. Let's suppose that we have "n" units in a figure of "b" sides. So, we have (sorry for my own notation and my own formulae): nEb = (n/2) [b + (n-2) (b-2)]. An arithmetic progession is a triangular number. So, we replace "b" by 3: nE3 = (n/2) [3 + (n-2) (3-2)] = (n/2) [3 + n-2] = (n/2) (n+1) = [n (n+1)]/2, which is Gauss' formula.

[TheNetkrot]

This is great it is the best I have found on the net about series.

[Algebrainiac]

8:21 wait so the students have never seen a geometric series or the sum from n=1 to infinity or a finite number of a1 r^n??? I thought maybe they may have at least done geometric series in Precal. Come on y’all 🤦🏻‍♂️ lol

[jisungyu]

She often skips an equation with a limit notation. I think that is what causes students confused about it.

[yalenasorokina]

Isn't Natalia Sorokina Quiet Genius @ Work, I'm a cosmonaut Illuminati confirmed

[Becinal]

Of strange zeros for oxygen around the k id volume called n

[dreia]

It looks to me that she is under some pressure of time

[siphilipe]

And good to be far from the cold of Siberia.