# Divergence of Series by Rearrangement

by Bernard August (Rowan University) and Thomas J. Osler (Rowan University)

College Mathematics Journal
May, 2002

Subject classification(s): Calculus | Single Variable Calculus | Series
Applicable Course(s): 3.2 Mainstream Calculus II

Assume that a series with non-negative terms converges to $$S$$. If from this assumption, a rearrangement of the series can be shown to converge to a different value $$S'$$, then the original series must have diverged. The author uses this result to show that a number of series diverge.

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