Lesson 18a - Integral Test and P-test

Example3continued

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Unformatted text preview: n) f ' ( n) n n 2 2 f ' ( n) (1 n)(1 n) n 1 1 n2 2 1 1 2 2 2 This means that the slope is 0 when n = 1 or ‐1. We only care about what happens when we go to infinity, so we find the slope of a value after n=1 (the furthest zero to the right) to get: f ' ( 2) (1 2)(1 2) 2 2 1 2 3 f ' ( 2) 25 This means that our function is decreasing when we are going towards infinity (negative slope). Example 3 Continued 2. We can see that the values of the function never become negative (the top is always positive, and the denomin...
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