$$f(x)=\sum_{n=1}^\infty{n!\over n^n}(2x-1)^n$$
How do we approach this question? I tried to use the ratio test and ended up with $|2x-1|$ times infinity...
2026-04-07 21:24:10.1775597050
Find the radius of convergence of the power series and its open interval of convergence I
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Hint: use sterlings formula for factorials:
$n! \sim \sqrt{2\pi n} \cdot (\frac{n}{e})^n$