MediumSeries

#1715 · Real Analysis · Series

Series convergence with parameters

Determine whether the following series is convergent or divergent, where $a$ is a proper fraction: $1 + rac{a(1-a)}{1^2} + rac{(1+a)a(1-a)(2-a)}{1^2 imes 2^2} + rac{(2+a)(1+a)a(1-a)(2-a)(3-a)}{1^2 imes 2^2 imes 3^2} + imes imes imes$

~15 minProof · checked by AIconvergencyratio test

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXI. Convergency and Divergency of Series, Examples XXI.b, No. 7

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