#1705 · Real Analysis · Series

Factorial series with power

Show that the series $1 + \frac{2 ^{p}}{2 !} + \frac{3 ^{p}}{3 !} + \frac{4 ^{p}}{4 !} + \dots$ is convergent for all values of $p$ .

~10 minProof · checked by AIconvergencyratio test

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXI. Convergency and Divergency of Series, Examples XXI.a, No. 19

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