RedAssign10[1].3 - Unit Sequences and Series Module The...

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Unit: Sequences and Series Module: The Direct Comparison Test [page 1 of 2] Introduction to the Direct Comparison Test [email protected] Copyright 2001, Thinkwell Corp. All Rights Reserved. 1663 –rev 06/15/2001 Use the direct comparison test to determine the convergence or divergence of an unfamiliar series by comparing it to a familiar one. It is possible to determine if a series converges or diverges by comparing it to a different series with which you are familiar. Since the test compares two series by directly examining their terms, it is called the direct comparison test . The first part of the direct comparison test deals with convergence. If you can show that each term of your unknown series is positive and less than or equal to its corresponding term in a known convergent series, then the unknown series must converge. The reason the series converges is because the terms are positive. That makes the sequence of partial sums an increasing sequence. In addition,
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