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Is there a formal term for the "status" of a series?
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I'm writing personal notes in Calculus 2. While writing the integral test's details as:

  1. If the integral from k to infinity of f(x) dx converges, then the sum from n=k to infinity of f(n) converges.
  2. If the integral from k to infinity of f(x) dx diverges, then the sum from n=k to infinity of f(n) diverges.

I just wrote it as "the status of the integral is the same as the sum" to make it more digestible when studying (fits me.)

Subsequently, I wondered if there's a more formal and universally understood term for the "status" of a series.

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2 months ago