# The Ratio Test Exercises

### Example 1

Apply the ratio test to the series. Determine if the series converges, diverges, or requires a different test.

For the series, find

- If
*L*is less than 1, the series converges. - If
*L*is greater than 1 (including infinity), the series diverges. - If
*L*is equal to 1, we need a different test.

### Example 2

Apply the ratio test to the series. Determine if the series converges, diverges, or requires a different test.

For the series, find

- If
*L*is less than 1, the series converges. - If
*L*is greater than 1 (including infinity), the series diverges. - If
*L*is equal to 1, we need a different test.

### Example 3

Apply the ratio test to the series. Determine if the series converges, diverges, or requires a different test.

For the series, find

- If
*L*is less than 1, the series converges. - If
*L*is greater than 1 (including infinity), the series diverges. - If
*L*is equal to 1, we need a different test.

### Example 4

For the series, find

- If
*L*is less than 1, the series converges. - If
*L*is greater than 1 (including infinity), the series diverges. - If
*L*is equal to 1, we need a different test.

### Example 5

For the series, find

- If
*L*is less than 1, the series converges. - If
*L*is greater than 1 (including infinity), the series diverges. - If
*L*is equal to 1, we need a different test.