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# 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

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 5

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.