#1884 · Real Analysis · Series

Shifted harmonic series

Test the series $\frac{1}{x} + \frac{1}{x + 1} + \frac{1}{x + 2} + \frac{1}{x + 3} + \dots$ for convergency or divergency, where $x$ is a positive fraction.

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H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXI. Convergency and Divergency of Series, Examples XXI.a, No. 18 (part 1)

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).