Determining Radius of Convergence of Power Series Find the radius of convergence for the following power series:



My workings:
$$\lim_{n\rightarrow ∞}|\frac{(n+1)! (x-1)^{n+1}}{2^{n+1}(n+1)^{n+1}}\centerdot \frac{2^nn^n}{n!(x-1)^n}|$$

$$=\lim_{n\rightarrow ∞}|\frac{1}{(1+1/n)^n}\centerdot \frac{x-1}{2}|$$

$$=\lim_{n\rightarrow ∞}|\frac{x-1}{2e}|$$

$|x-1|&lt;2e$

$|x|&lt;2e+1$; Therefore, $R=2e+1$?

However, my answer is incorrect, as the answer given is $R=2e$ 

Could any of you tell me where did I go wrong?
Your calculation is fine, up to the very last step. That is, once, you have $\left | x-1 \right |\leq 2e$, you're done because the series is centered at $x_{0}=1$, so $R=2e$
Actually, you got the answer right. The disk is just not centered at the origin, since the series is centered at 1.