# DETERMINE THE GEOMETRIC SERIES IS CONVERGENT OR DIVERGENT WORKSHEET

Decide whether each infinite geometric series is convergent or divergent. State the sum of the series, if it exists.

Problem 1 :

1 - 1/3 + 1/9 - …

Solution

Problem 2 :

2 - 4 + 8 - …

Solution

State whether each infinite geometric series is convergent or divergent.

Problem 3 :

t1 = -3, r = 4

Solution

Problem 4 :

t1 = 4, r = -1/4

Solution

Problem 5 :

125 + 25 + 5 + …

Solution

Problem 6 :

(-2) + (-4) + (-8) + …

Solution

Problem 7 :

243/3125 - 81/625 + 27/25 - 9/5 + ….

Solution

1)  Convergent, S= 3/4

2) Divergent, does not exists.

3)  The value of r = 4.  So, the given series is divergent.

4)  r = -1/4. So, the given series is convergent.

5)  r = 1/5.  So, the given series is convergent.

6)  r = 2. So, the given series is divergent.

7) r = -5/3. So, the given series is divergent.

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