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Section 8.2: Infinite Series

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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  1. Section 8.2: Infinite Series

  2. 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 ??

  3. Informal Definition A series is sequence added up.

  4. Formal Definition A series converges if the sequence of partial sums converges.

  5. Example

  6. Definition is a geometric series.

  7. Theorem Diverges if Convergesto if

  8. Proof: If and only if

  9. This solves Zeno’s paradox!!

  10. Diverges

  11. Telescoping Series Use Partial Fractions

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