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Convergence of sum(1/(1+n^2)) using the integral test resulting in arctan improper integral.

Автор: Zak's Lab

Загружено: 2020-12-15

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We test the convergence of the sum(1/(1+n^2) using the integral test. In this case, we arrive at integral test resulting in arctan(x), which has to be evaluated from 1 to infinity. When we integrate 1/(1+x^2) on zero to infinity, we find the inverse tangent of infinity is just pi/2, and the integral comes out to a finite number, proving that the series converges. Integral test Calculus 2 problem giving arctan improper integral.

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Convergence of sum(1/(1+n^2)) using the integral test resulting in arctan improper integral.

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