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Welcome, to week 3 of Sequences and
Series.

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[MUSIC].

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In the first week of this course, in week
1, we met sequences.

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And last week, in week 2, we met series.

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Now, considering that the name of this
course is sequences and series.

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Does that mean we're done with this
course,

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that we've covered everything we meant to
cover?

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Not at all, we're just getting started.

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Now that we know about sequences and
series, it's time

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to really dig in, and do something with
these things.

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In particular,

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we're going to focus on convergence tests.

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Given a series, does a converge or
diverge?

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We've seen a little bit of this already,
we've

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learned about the nth term test that tells
us to

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look at the limit of the nth term of a

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series and if that limits not 0, the
series diverges.

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We've learned about geometric series, we
learned about comparison

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tests, but there's way more convergence
tests to cover.

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This week, we're going to be looking at
these fancier convergence tests.

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We're going to be focusing

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on the ratio test, the root

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test and the integral test.

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It'll be a lot of fun.

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[SOUND]