• convergent series
• divergent series
• infinity
Convergent and Divergent Series
A. Determine whether the infinite geometric series
is convergent or divergent.
729 + 243 + 81 + …
Find the value of r.
Answer: Since
the series is convergent.
A. Determine whether the infinite geometric series
is convergent or divergent.
343 + 49 + 7 + …
A. convergent
B. divergent
1.
2.
A
B
Convergent and Divergent Series
B. Determine whether the infinite geometric series
is convergent or divergent.
2 + 5 + 12.5 + …
Answer: Since 2.5 > 1, the series is divergent.
B. Determine whether the infinite geometric series
is convergent or divergent.
4 + 14 + 49 + …
A. convergent
B. divergent
A
0%
A
B
0%
B
1.
2.
Sum of an Infinite Series
A. Find the sum of
exists.
, if it
Find the value of r to determine if the sum exists.
the series diverges and the sum does
not exist.
Answer: The sum does not exist.
A. Find the sum of the infinite geometric series, if
it exists.
2 + 4 + 8 + 16 + ...
A. 4
A
0%
B
0%
D. no sum
A
B
C
0%
D
D
C. 2
A.
B.
C.
0%
D.
C
B. 1
Sum of an Infinite Series
B. Find the sum of
, if it exists.
the sum exists.
Now use the formula for the sum of an infinite
geometric series.
Sum formula
Sum of an Infinite Series
a1 = 3, r =
Simplify.
Answer: The sum of the series is 2.
B. Find the sum of the infinite geometric series, if
it exists.
A. 4
D. no sum
0%
B
A
0%
A
B
C
0%
D
D
C. 1
C
B. 2
A.
B.
C.
0%
D.
Infinite Series in Sigma Notation
Evaluate
Sum formula
a1 = 5, r =
Simplify.
Answer: Thus,
Evaluate
.
A. 6
A
0%
0%
B
D. no sum
A
B
C
0%
D
D
C.
A.
B.
C.
0%
D.
C
B. 3