ns All Over the Place

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

((3n^3+2n-1)/(2n^3+(1/n)))^n

converges can be found using the Root Test:

the limit as n goes to infinty of the nth root of ((3n^3+2n-1)/(2n^3+(1/n)))^n = the limit as n goes to infinity of (3n^3+2n-1)/(2n^3+(1/n)) = 3/2

so the series diverges.

Copyright © 1996 Department of Mathematics, Oregon State University

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