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Testing for Convergence or Divergence

Testing for Convergence or Divergence of a Series Many of the series you come across will fall into one of several basic types. Recognizing these types will help you decide which tests or strategies will be most useful in finding whether a series is convergent or divergent. If nahas a form that is similar to one of the above, see whether you can use the comparison test: Geometric Series = 11nnar convergent if 1<r divergent if 1 r p-Series =11npn convergent if 1>p divergent if 1 p Example: =+121nnn Pick 21nbn=(p-series) 2211nnnan +=, and =121nn converges, so by (i), =+121nnn converges. Some series will obviously not converge recognizing these can save you a lot of time and guesswork.

Testing for Convergence or Divergence of a Series . Many of the series you come across will fall into one of several basic types. Recognizing these types will help you decide which tests or strategies will be most useful in finding

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