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The Relation Between the Root and Ratio Tests

by David Cruze-Uribe (Trinity College)

This article originally appeared in:
Mathematics Magazine
June, 1997

Subject classification(s): Calculus | Single Variable Calculus | Series
Applicable Course(s): 3.0 Calculus | 3.2 Mainstream Calculus II | 4.11 Advanced Calc I, II, & Real Analysis

For series with non-zero terms, the Root Test is interpreted in terms of the geometric mean of the ratios of successive terms (in absolute value). The author also consders the test obtained by substituting the arithmetic mean for the geometric mean.

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Capsule Course Topic(s):
Sequences and Series | Tests For Convergence and Divergence
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