5.5 Alternating Series (p.496–502) HW: P. 505: 250–257 all, 261—264 all, 266, 267

5.6 Ratio and Root Tests (p.509–519) HW: P. 522: 317–320 all, 323, 325, 328, 329–335 odd, 349, 351

Webwork: Alternating Series & Ratio and Root Tests due Tuesday

Notes from lecture and office hours: https://www.dropbox.com/s/i58xxrwn4ioapmb/Note%20Apr%2022%2C%202020.pdf?dl=0

Sorry, the lecture wasn’t recorded (I’ll see if I can work on my Webex recording problem for next week’s lectures). I’ve linked lots of videos below.

On Monday, we’ll see a couple more examples illustrating the ratio test and root tests before we move on to Power Series.

5.5 Alternating Series (and absolute/conditional convergence)

  • This video (5 minutes) shows an introduction to the alternating series test, along with a few examples.
  • This video (8 minutes) shows an introduction to absolute versus conditional convergence, along with a few examples.

5.6 Ratio and Root Tests

  • This video (5  minutes) shows an example applying the ratio test to determine the convergence of a series.
  • This video (5 minutes) shows a second example applying the ratio test.
  • These two videos show one particular example twice, once using the limit comparison test (7 minutes) and one using the ratio test (6 minutes). The first video includes an introduction about why the other tests would not appropriate for this example.
  • This video (7 minutes) provides an introduction to the root test, along with a few examples.

The same account mathispower4u has lots and lots of other good examples too.

More alternating series examples:

 

More absolute/conditional convergence examples:

More ratio test examples:

In these examples the ratio test is conclusive. Don’t forget: if you get 1 when you evaluate your limit, you’ll have to use another test.

More root test examples:

Just like in the videos for the ratio test above, in these examples the root test is conclusive. Don’t forget: if you get 1 when you evaluate your limit, you’ll have to use another test.