What is the Root Test for Convergence of an Infinite Series?

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What is the Root Test for Convergence of an Infinite Series?

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Answer 1 · 2014-10-17T01:07:43

Root Test

If #lim_{n to infty}root[n]{|a_n|}<1#, then #sum_{n=1}^inftya_n# converges.
If #lim_{n to infty}root[n]{|a_n|}>1#, then #sum_{n=1}^inftya_n# diverges.
If #lim_{n to infty}root[n]{|a_n|}=1#, then it is inconclusive.

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What is the Root Test for Convergence of an Infinite Series?

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