What follows below reflects uncategorized recent activity in the courses I am teaching, with the most recent activity at the top. This information can be categorized by course and type by selecting the "courses" link above.

## Ratio Test

Section:
9.4
Date:
Wednesday, October 6, 2010 - 14:00 - 15:00

Math 2300 Section 005 – Calculus II – Fall 2010

9.4 Ratio Test Examples – October 6, 2010

1. What does the ratio test say about the series?

Solution:

and so the ratio test says nothing about the series. Of course, we already know that the harmonic series is divergent.

## Comparison Test

Section:
9.4
Date:
Tuesday, October 5, 2010 - 14:00 - Wednesday, October 6, 2010 - 15:00

Math 2300 Section 005 – Calculus II – Fall 2010

9.4 Comparison Test Examples – October 5, 2010

1. Use the comparison test to determine if the given series converges or diverges.

Solution: Since

and we know the -series

converges, the given series also converges.

## Integral Test

Section:
9.3
Date:
Monday, October 4, 2010 - 14:00 - 15:00

Math 2300 Section 005 – Calculus II – Fall 2010

9.3 Integral Test Examples – October 4, 2010

1. What does Theorem 9.2 say about the convergence or divergence of the series?

Solution: Since the series terms are of the form , and the limit of these terms as is 2 (not zero), we know that this series diverges.

2. What does Theorem 9.2 say about the convergence or divergence of the series?

## Exam 2 Review 1

A review sheet for exam 2 is now available, as an attachment to this post.

## LA Information

Date:
Wednesday, October 6, 2010 - 18:00 - 19:00

There is an informational session about becoming a Learning Assistant (LA) on Wednesday, October 6 at 6PM in UMC235. Applications for Spring 2011 will be available October 6 - October 20.

If you are interested in attending the informational session, e-mail olivia.holzman@colorado.edu

## Fibonacci Sequence Video

Someone pointed this out to me on YouTube. It's a video about the Fibonacci Sequence.

## Geometric Series

Section:
9.2
Date:
Friday, October 1, 2010 - 14:00 - 15:00

Math 2300 Section 005 – Calculus II – Fall 2010

9.2 Geometric Series Notes – October 1, 2010

A tip on recognizing geometric series: Many times when you're using convergence comparison tests, the series you use for comparison is either a -series or a geometric series. In the first case, we know that

converges for and diverges for . In the second case, the geometric series in question may be more challenging to pick out. For instance, when you have

you may either view this as the geometric series

where and , giving from the formulas for geometric series that

Or (and this may seem odd at first, but I think it yields faster computations) view this as the geometric series

where and , except that the first term needs to be removed (since the series in question has no 1). So, we also have

## Webwork 9.2 Hints

Math 2300 Section 005 – Calculus II – Fall 2010

Hints for Webwork Section 9.2

Most of the Webwork problems for this section simply use the notions of geometric series that we developed in class. There are a few, however, that are challenging and require you to put a lot of thought in to setting up the series.

5. Consider a similar example. Us math folk really like coffee. Assume that at the start of each day I drink 300mg of caffeine. Also assume that the “halflife” of this caffeine in my system is 7.5 hours. So, in 7.5 hours I will effectively have 150mg of caffeine in my system, and in 15 hours that will be halved again and I will now have 75mg of caffeine in my system. Notice that at 24 hours (a full day after my last sip of coffee) I still have some caffeine in my system. How much? The answer: I take my initial amount and multiply it by half for each period of 7.5 hours. And since 24/7.5 of those periods happen in 24 hours, we find that I have

of caffeine in my system after 24 hours. At that instant, I drink another 300mg of caffeine and I now have

## Sequence and Series Quiz

Due Date:
Friday, October 1, 2010 - 16:00 - Monday, October 4, 2010 - 16:00

This quiz is due on Monday at 4PM. Obviously, only questions 1 and 2 count for credit. Due to my current lack of creativity, there is no replacement question on this quiz.

## Worksheet 5

The solutions are posted to worksheet #5