Section 8.2: Infinite Series

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# Section 8.2: Infinite Series - PowerPoint PPT Presentation

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

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.

Formal Definition

A series converges

if the sequence of partial sums converges.

Definition

is a geometric series.

Theorem

Diverges if

Convergesto if

Proof:

If and only if

Telescoping Series

Use Partial Fractions