Lesson 18a - Integral Test and P-test

Thismeanswecancomparetheseriestotheintegral 1 dn lnn

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Unformatted text preview: f converges, then so does the series. 1 Example 1 1 Consider the following series: n 1 n 1. an decreases (we know that 1/n gets smaller as n gets larger) 2. an is always positive (as n is always positive) 3. f(n) = an is a continuous function (it is only discontinuous at n=0, but we are starting from n = 1). This means we can compare the series to the integral: 1 dn ln(n) 1 n 1 1 n dn ln() ln(1) 1 This means both the integral and the series diverge by the integral test! (Note that the terms go to zero, but the series still diverges) Example 2 1 Consider the following series: 2 n 1 n 1 1. an decreas...
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