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 - …

Problem 2 :

2 - 4 + 8 - …

State whether each infinite geometric series is convergent or divergent.

Problem 3 :

t₁ = -3, r = 4

Problem 4 :

t₁ = 4, r = -1/4

Problem 5 :

125 + 25 + 5 + …

Problem 6 :

(-2) + (-4) + (-8) + …

Problem 7 :

243/3125 - 81/625 + 27/25 - 9/5 + ….

Answer Key

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.