The Raabe’s test is applicable if the D’Alembert Ratio test fails.
This series converges if L > 1.
Diverges if L < 1.
Test fails if L = 1.
Example
Test for convergence for the series
Solution
First, using D’Alembert ratio test, the test fails. Click the above on how to use the ratio test.
Next, we use the Raabe’s test.
Hence the series converges.