1. Infinite Geometric Series
Feb 13th 2015

2. Zeno’s Paradox
Can we clap our hand?

3. Convergent Series
Consider the series … S5 = S7 = S9 = S11 = S13 = S15 = S17 =

4. Convergent Series The sum of this series converges at 8
Consider the series … S5 = 7.75 S7 = S9 = S11 = S13 = S15 = S17 =
The sum of this series converges at 8

5. convergent series
a series with an infinite number of terms, in which the sequence of partial sums approaches a fixed value

6. We know this does not happen for all series so what makes some of them convergent?
Consider the series …
Does is converge?

7. Divergent Series
a series with an infinite number of terms, in which the sequence of partial sums does not approach a fixed value

8. Only well behaved series are convergent

9. Infinite Geometric Series
The formula for the sum of a geometric series is When r is less then 1 we use this equivalent equation

10. Infinite Geometric Series
When r is between -1 and 1

11. Infinite Geometric Series Equation

12. Homework
Pg 63 #6-11,18,19