1. GEOMETRIC SERIES Feb 11 th 2015

2. Geometric Series is called the partial sum

3. Equation First, call the whole sum "S": S=a + ar + ar 2 +... + ar (n-2) + ar (n-1) Next, multiply S by r: Sr=ar + ar 2 + ar 3 +... + ar (n-1) + ar n

4. Now subtract the two equations S − Sr = a − ar n

5. Almost there Factor out S and a: S(1−r) = a(1−r n ) Divide by (1-r): S = a(1−r n )/(1−r)

6. Finally we have the equation for a Geometric series (For r not equal to 1)

7. We can rearrange to get another equation

8. New Equation

10. Example: Find the sum of the finite geometric series: 3 – 6 + 12 – 24 + 48 – 96

12. Example: Given 5 + 10 + 20 +…+ 1280 find its sum. (can be done two ways)

13. Homework Pg 53 #1-8