1. Ch.9 Sequences and Series
Section 5 –Geometric Series Part

2. Definition: Geometric Series
The sum of a finite geometric series
where is the first term, r is the common ratio, and n is the number of terms.

3. EXample What is the sum of the finite geometric series?
…+3072

4. EXample
What is the sum of the finite geometric series?

5. The Soldier’s Reasonable Request
A soldier rescued his king. As a reward, he could have anything “within reason.” The soldier requested a chessboard with a single kernel of wheat on the first square, two kernels of wheat on the second, then four, then eight, and so on for all 64 squares. How many kernels of wheat did the soldier request?

6. Definition: Infinite Geometric Series
An infinite geometric series with first term and common ratio < 1 has a finite sum
An infinite geometric series with does not have a finite sum.

7. Concept: Sum of an infinite series
If has a sum, that means that the sequence of
partial sums
converges to a number S as n gets very large.
When an infinite series does not converge to a sum, the series diverges. An infinite geometric series with diverges.

8. EXample
Does the series converge or diverge? If it converges, what is the sum?

9. EXample
Does the series converge or diverge? If it converges, what is the sum?