#1713 · Real Analysis · Series

Another factorial-power series

Determine the values of $x$ for which the following series is convergent or divergent: $1 + \frac{1}{2} x + \frac{2 !}{3 ^{2}} x^{2} + \frac{3 !}{4 ^{3}} x^{3} + \frac{4 !}{5 ^{4}} x^{4} + \dots$

~12 minProof · checked by AIRatio testFactorialsExponential limit

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXI. Convergency and Divergency of Series, Examples XXI.b, No. 5

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