COMPARISON TEST Meaning and
Definition
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The comparison test is a method used in mathematics to analyze the convergence or divergence of an infinite series. In particular, it is employed to determine the behavior of a given series by comparing it to another known series whose behavior is already understood.
To apply the comparison test, two series must be considered: the given series and a known "comparison series." The comparison series is typically chosen to be a simpler or more well-known series whose properties are already established.
The concept behind the comparison test is straightforward. If the comparison series converges and the terms of the given series are always larger or equal to the corresponding terms of the comparison series, then the given series must also converge. On the other hand, if the comparison series diverges and the terms of the given series are always smaller or equal to the terms of the comparison series, then the given series must also diverge.
The comparison test is commonly used in calculus, particularly when dealing with positive series, where all terms are greater than or equal to zero. It provides a convenient way to determine convergence or divergence without relying on more complicated methods, such as the integral test or the ratio test. However, it should be noted that the comparison test only establishes a relative behavior between the given series and the comparison series, and does not provide information about the actual values of convergence or divergence.
Common Misspellings for COMPARISON TEST
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Etymology of COMPARISON TEST
The word "comparison" originated from the Latin term "comparatio", which translates to "a comparing" or "compared with". It is derived from the verb "comparare", meaning "to compare" or "to pair together".
The word "test", on the other hand, comes from the Old French term "teste" or "test", which refers to a vessel or pot used for melting or assaying metals. This term was used metaphorically to describe any critical examination or trial. It eventually entered Middle English as "test" and evolved to its current meaning as a trial or evaluation.
Thus, the term "comparison test" essentially implies a trial or examination where items or entities are compared or paired together to determine their similarities, differences, or relative qualities. In various fields or contexts, the comparison test may be used to assess the performance, suitability, effectiveness, or other attributes of different elements being analyzed.
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