@mes's thread

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.

#math #calculus #series #divergence #education