- Your "homework" for section 11.3 will become part of the next exam
(which will cover through 11.3). One of these problems from 11.3 will
appear on the exam: pp. 563-556, #5, 15, 17, 32, 40, 48, 82; you'll
also want to practice some of the problems from #49-74.
- Majors: there will be a banquet on the 6th of November, at 6:00 pm (the annual Sehnert lecture); I hope that you will attend. There will be a sign-up sheet in the department office (not yet, but soon). Just a heads-up!
-
This theorem tells us that if a sequence isn't asymptotic to the x-axis, we can forget about its partial sums converging.
Finally, series behave the way we'd hope (notice the suppression of the limits on the summations):
- Examples:
- #52, p. 556
- #7, p. 554
- #8, p. 554 (compare to Taylor series error bound)
- concerns several different means of testing for convergence of
series with all positive terms (obviously, if we're dealing with series
of all negative terms, similar results are going to apply).
- We're not so concerned with the actual limits (that is the values
of the series) as we are with the convergence (or divergence) of the
series.
- Theorems:
Theorem 3 is just a corollary of Theorem 2, where the integrals are the obvious power functions:
- Examples:
- Integral Test: #9, 10, p. 563
- Comparison Test: #20, p. 563
- Limit Comparison Test: #34, p. 563