Excluding these cases, the ratio test can be applied to determine the radius of convergence.

A good score in the quick ratio test is usually an indication of a healthy business.

Since this is less than 1, the ratio test shows that the sum converges.

He also created his ratio test, a test to see if a series converges.

These series converge for x in , as may be seen by applying the ratio test to the recurrence.

The radius of convergence is 1/e, as may be seen by the ratio test.

Below is a proof of the validity of the original ratio test.

As seen in the previous example, the ratio test may be inconclusive when the limit of the ratio is 1.

Extensions to ratio test, however, sometimes allows one to deal with this case.

Note that comparison functions are necessarily entire, which follows from the ratio test.