Change the negative terms to positive by taking the absolute value of the terms. If the new series converges, then so does the old one, by the Absolute Convergence Test.

With an *n* in the power of the term, the
Root Test can cancel that
power
of *n*, so try that. Also, the Ratio
Test often can be useful in such
circumstances.

For instance,whether or not the sum of

converges can be found using the Root Test:

so the series diverges.

Copyright © 1996 Department of Mathematics, Oregon State University

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