#1712 · Real Analysis · Series

Convergence involving factorials and powers

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

~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. 4

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