Lesson 20a - Comparison Test


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Unformatted text preview: get rid of positive terms in the numerator, and negative terms in the denominator: 2n 2 n 1 2n 2 n n 3 5n 2 2 n 3 2 n 1 n 1 Example 1 We are a little closer, next we know that we can make the numbers smaller by changing negative terms in the numerator to become larger negative terms, and changing positive terms to become larger positive terms in the denominator: 2n 2 n 1 2n 2 n 2n 2 n 2 n2 1 1 n3 5n 2 2 n3 2 n3 2n3 3n3 3 n n 1 n 1 n 1 n 1 n 1 The latter series diverges, and since our original series is larger, we have: 2n 2 n 1 n 3 5n 2 2 n 1 Diverges by the comparison test. Example 2 Determine if the following series converges or diverges: ln(n) n n n 1 First we determine our guess by comparing the largest terms. The problem is that ln is hard to compare to...
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This note was uploaded on 02/07/2014 for the course MATH 1004 taught by Professor Mark during the Summer '00 term at Carleton CA.

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