#1693 · Real Analysis · Series

General Alternating Product Series

Determine whether the series $\frac{1}{x y} - \frac{1}{( x + 1 ) ( y + 1 )} + \frac{1}{( x + 2 ) ( y + 2 )} - \frac{1}{( x + 3 ) ( y + 3 )} + \dots$ is convergent or divergent, where $x$ and $y$ are positive quantities.

~5 minProof · checked by AIalternating seriesLeibniz test

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXI. Convergency and Divergency of Series, Examples XXI.a, No. 3

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