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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.
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