Term test

In mathematics, the nth-term test for divergence[1] is a simple test for the divergence of an infinite series:

  • If or if the limit does not exist, then diverges.

Many authors do not name this test or give it a shorter name.[2]

When testing if a series converges or diverges, this test is often checked first due to its ease of use.

In the case of p-adic analysis the term test is a necessary and sufficient condition for convergence due to the non-archimedean triangle inequality.

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