Basic Analysis I — Real Analysis · Problem 2.2.16

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · convergence-tests

Problem

Prove that {(n!)1/n}n=1∞\{(n!)^{1/n}\}_{n=1}^\infty is unbounded. Hint: Show that for every C>0C > 0, {Cnn!}n=1∞\left\{\dfrac{C^n}{n!}\right\}_{n=1}^\infty converges to zero.

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