1. Section 8.2: Infinite Series

2. Zeno’s Paradox Can you add infinitely many numbers ?? 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.

3. Informal Definition A series is sequence added up.

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

5. Example

6. Definition is a geometric series.

7. Theorem Diverges if Converges to if

8. Proof: If and only if

10. This solves Zeno’s paradox!!

13. Diverges

14. Telescoping Series Use Partial Fractions