#1706 · Real Analysis · Series

Cauchy's root test condition

Show that the infinite series $u_{1} + u_{2} + u_{3} + u_{4} + \dots$ is convergent or divergent according as $lim_{n \to \infty} n u_{n}$ is $< 1$ , or $> 1$ .

~10 minProof · checked by AIroot testconvergency

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXI. Convergency and Divergency of Series, Examples XXI.a, No. 20

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