1) A geometric series is the expression of the sum of terms in a geometric sequence. The sum of a finite geometric series can be calculated using the formula Sn = a(1 - r^n)/(1 - r) where a is the first term, r is the common ratio, and n is the number of terms. 2) Geometric series converge when the absolute value of the common ratio r is less than 1, and diverge when the absolute value of r is greater than 1. 3) The homework assignment includes evaluating example geometric series, determining whether other series converge or diverge, and completing a worksheet to review for a test on geometric series.

1. Homework Questions

2. Geometric Series
Mrs. Ramsey

3. Geometric Series
A geometric series is the expression of
the sum of the terms of a geometric
sequence.
Sum of a finite Geometric Series:
r
ra
S
n
n
−
−
=
1
)1(1

4. Evaluate the series
1. 3 + 6 + 12 + 24 + 48 + 96
2. - 45 + 135 – 405 + 1215 – 3645
3. 81
1
27
1
9
1
3
1
+++

5. Convergence:
When |r| < 1, the series converges
Gets closer and closer to the sum
When |r| > 1, the series diverges
Approaches no limit

6. Determine convergence or divergence:
1.
2.
3.
4.
...
9
1
3
1
1 −+−
...
25
1
5
1
1 +++
∑
∞
=
−
1
1
)2(5
n
n
1684 ++

7. Sum of Infinite Geometric Series
1.
2.
...
8
1
4
1
2
1
1 ++++
r
a
S
−
=
1
1
...
8
3
4
3
2
3
3 +−+−

8. Homework
WORKSHEET 
Get a jump on your review for your
test…it’s TOMORROW!