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Section 8.2: Infinite Series PowerPoint PPT Presentation


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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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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.


Formal Definition

A series converges

if the sequence of partial sums converges.


Example


Definition

is a geometric series.


Theorem

Diverges if

Convergesto if


Proof:

If and only if


This solves Zeno’s paradox!!


Diverges


Telescoping Series

Use Partial Fractions


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