For what $x \in \mathbb{R}$ does the series $\sum_{n=0}^{\infty} n!x^{n}$ converge?
How would you prove this? Does the ratio test apply?
2026-04-18 13:40:14.1776519614
For what $x \in \mathbb{R}$ does the series $\sum_{n=0}^{\infty} n!x^{n}$ converge?
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Yes, the ratio test applies and yields that it converges for $x=0$ only.
Let me know if you need more details.