#1704 · Real Analysis · Series

Factorial-like power tower series

Determine whether the series $1 + \frac{1}{2 ^{2}} + \frac{2 ^{2}}{3 ^{3}} + \frac{3 ^{3}}{4 ^{4}} + \frac{4 ^{4}}{5 ^{5}} + \dots$ is convergent or divergent.

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H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXI. Convergency and Divergency of Series, Examples XXI.a, No. 16

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