Welcome to week four, of sequences and series.
Thus far in the course, we've been focusing on series where all the terms are
positive, and it's a hugely helpful simplifying assumption to make.
because if all the terms are positive, then the only way
the series can fail to converge is if it diverges to infinity.
I don't have to worry about oscillating behavior at all.
Well this week, we throw that assumption away.
This week, we're going to consider series where some of
the terms are positive, some of the terms are negative.
And in particular, we're going to focus in on alternating series,
where the SIGN, the sign of the terms, are flip flopping.
Maybe the first term's negative, next term's positive,
negative, positive, negative, positive, back and forth like that.
There's a rich theory
for alternating series. Finally, I want to say hang
in there We are more than halfway through this course now, and I know that you can
make it to the end. Good luck!
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