Your homework for section 11.3 is due next Thursday.
Homework for 11.3 will be pushed back until 10/22.
Homework for 11.4 will be pushed back until 10/29.
We'll do 11.5 next time (no quiz, as I forgot to make up the
worksheet!;)
Exam revisions are due today.
Section 11.4: Absolute and Conditional Convergence
Once again, our mission here is not necessarily the value of the
series, but may be simply knowledge of whether it converges or
not.
That being said, Theorem 2 below does give
us some help in determining the value of (or at least bounds
on the value of) the series.
How do they reach the conclusion that the sum is positive and at most
a1?
Let's think of a couple of examples of
Series that converge absolutely, and
Series that don't.
Examples:
#2, p. 570
#6, p. 570
#8, p. 570
#18, p. 570:
where
is the size of the term (i.e. positive).
#27, p. 570
It turns out that conditionally convergent series can have
their terms rearranged to converge to any limit you
like. Hmmm.... Is this the end of commutativity?!
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