1. 11-6. Convergent Geometric Series
How do we know when a series converges?

2. Sums of geometric series either diverge or converge
Example #1:
…………………
A few partial sums are: (Don’t need to write)
S1 = 2
S2 = = 6
S3 = = 14
S4 = = 30
S5 = = 62
The sums are increasing!

3. Sums of Geometric series either diverge or converge
Example #2
………..
A few partial sums are: (Don’t need to write)
S1 = 8
S2 = = 12
S3 = = 14
S4 = = 15
S5 = ½ = 15.5
The sums are getting larger, but seem to be less than 16.

4. Diverging or converging sums
The value of r, the common ratio, determines the behavior of the sum.
Example #1: r = 2; sum diverges
Example #2: r = ½ ; sum converges
When a series converges.
The absolute value means that it can be POSITIVE or NEGATIVE (but will be a true fraction)

5. Equation for the sum of a convergent geometric series
Remember to check your “r” value!!!!
Clue: If the Series gets smaller you can get a sum. If it’s getting larger it will NOT have a sum!

6. Ex) Determine if the series converges. If so, find the sum.
each term is getting smaller & smaller
so it has a sum

7. Ex) Determine if the series converges. If so, find the sum.…
r = 10
> 1
DIVERGES!!!
(Hint: The series is getting bigger
so it will be NO SUM!)

8. YOYO) Determine if the series converges. If so, find the sum.
8 – – 1 + …
so it has a sum

9. Homework PG. 594-595 Q1-10 #1-9 odd, Pg. 601 S1-S4
(S is for slow instead of Q quick) The S problems are review from the current chapter