Taylor expansion of $\ln\left(1+\frac1x\right)$

Question

If we apply maclaurin series for $\ln\left(1+\dfrac1x\right)$, we get $\ln(\infty)$. Is this correct?

Answer 1

Taylor Series are $k$ degree polynomial approximations for k-times-differentiable functions.

$f(x)=\ln(1+\frac{1}{x})$ neither exists nor is differentiable at $x=0$, therefore it does not have a Maclaurin Series.

However, at $x=1$, it is infinitely differentiable, so the Taylor Series can be computed.