Example: The ratio test as well as the root test show that the series converges.
We have to check the lim sup of the expression Clearly, the lim sup of this expression is equal to 1/2. Hence, by the ratio test the series converges absolutely.

The root test for this series, of course, gives the same result. However, it is much easier to compute the limit of the above expression rather than computing it for the expression resulting in the root test.

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