FOR WHAT VALUE OF X DOES THE GEOMETRIC SERIES CONVERGE WORKSHEET

Each of the following represents an infinite geometric series. For what values of x will each series be convergent?

Problem 1 : 

5 + 5x + 5x² + 5x³ + …

Solution

Problem 2 :

1 + x/3 + x²/9 + x³/27 + …

Solution

Problem 3 :

2 + 4x + 8x² + 16x³ + …

Solution

Problem 4 :

The infinite series given by

1 + 3x + 9x² + 27x³ + …

has a sum of 4. What is the value of x?

List the first four terms of the series.

Solution

Problem 5 :

Dominique and Rita are discussing the series

-1/3 + 4/9 - 16/27 + ...

Dominique says that the sum of the series is -1/7.

Rita says that the series is divergent and has no sum.

a. Who is correct?

b. Explain your reasoning.

Solution