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Welcome to week four, of sequences and
series.

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Thus far in the course, we've been
focusing on series where all the terms are

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positive, and it's a hugely helpful
simplifying assumption to make.

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because if all the terms are positive,
then the only way

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the series can fail to converge is if it
diverges to infinity.

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I don't have to worry about oscillating
behavior at all.

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Well this week, we throw that assumption
away.

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This week, we're going to consider series
where some of

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the terms are positive, some of the terms
are negative.

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And in particular, we're going to focus in
on alternating series,

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where the SIGN, the sign of the terms, are
flip flopping.

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Maybe the first term's negative, next
term's positive,

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negative, positive, negative, positive,
back and forth like that.

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There's a rich theory

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for alternating series.
Finally, I want to say hang

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in there We are more than halfway through
this course now, and I know that you can

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make it to the end.
Good luck!

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