Integral Test for Convergence
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(By Kelsey Norman with HTML code from Prof. Gregory V. Bard)
\textrm{Integral Test for Convergence: Suppose that } f(x) \textrm{ is a continuous, positive and decreasing function }
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\textrm{ on the interval } [k, \infty ) \textrm{ and that } f(n) = a_n, \textrm{ then }
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1. \textrm{ If } \int_k^\infty f(x) \, dx \textrm{ is convergent, so is } \sum_{n = k}^\infty a_n.
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2. \textrm{ If } \int_k^\infty f(x) \, dx \textrm{ is divergent, so is } \sum_{n = k}^\infty a_n.
Last modified on July 17th, 2017.