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In testing ∑1 / n^2 for convergence, a student evaluates ∫0^∞ n^-2 d n=-.n^-1|0 ^∞= 0 ∞=∞and concludes (erroneously) that the series diverges. What is wrong? Hint: Consider the area under the curve in a diagram such as Figure 6.1 or 6.2 This example shows the danger of using a lower limit in the integral test. | Numerade
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