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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.3 Convergence Tests: All Series, #30 · Calculus · Series

Prove that this series converges

Prove that this series converges. Its sum is $π /2$ .
$\int_{0}^{π} \frac{sin x}{x} d x + \int_{π}^{2 π} \frac{sin x}{x} d x + \dots = \int_{0}^{\infty} \frac{sin x}{x} d x .$

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.3 Convergence Tests: All Series, #30

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