Published: 26 Jun 2026 › Updated: 26 Jun 2026
Theorem 1 and the Test for the Divergence of Infinite Series
In this video, I go over Theorem 1, which states that the terms of a convergent series approach zero. Conversely, if the terms don't approach zero, the series diverges, hence providing a useful test for divergence. I prove Theorem 1 by re-arranging the n-th term as a difference of two partial sums, which, since they are convergent, are equal and cancel out; thus proving the theorem.
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