Lesson 18a - Integral Test and P-test

An isalwayspositive 3 fnan

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Unformatted text preview: ator is always positive). 3. f(n) = an is a continuous function (we cannot get denominators of 0) Since the conditions are met, we can take the integral: n 1 1 1 2 n 2 1 dn 2 ln(n 1) 1 2 ln() 2 ln(2) 1 n 1 dn ln(n 2 1) n2 1 2 1 1 Therefore the series diverges by the Integral Test. P‐Test 1 Consider the following series: p n 1 n 1. an is decreasing (denominator is getting larger as n goes to infinity, numerator constant) 2. an is always positive 3. f(n) = an is a continuous function (as long as n starts with a number greater than 0) This...
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