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Section 8.2: Infinite Series

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Section 8.2: Infinite Series. Zeno’s Paradox. You can’t actually get anywhere because you always have to cover half the remaining distance! You have to do half, then half that.. etc. Can you add infinitely many numbers ??. Informal Definition A series is sequence added up.

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Presentation Transcript
slide2
Zeno’s Paradox

You can’t actually get anywhere because you always have to cover half the remaining distance!

You have to do half, then half that.. etc.

Can you add infinitely many numbers ??

slide3
Informal Definition

A series is sequence added up.

slide4
Formal Definition

A series converges

if the sequence of partial sums converges.

slide6
Definition

is a geometric series.

slide7
Theorem

Diverges if

Convergesto if

slide8
Proof:

If and only if

slide14
Telescoping Series

Use Partial Fractions

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