Graph of the Maclaurin Series of $\ln (1+x)$ vs the graph of the real function $\ln (1+x)$
The Maclaurin Series for $\ln (1+x) = \frac{(-1)^{n+1} x^n}{n}$
Performing the Ratio Test to determine the convergence criterion, I got $x$ and for it to converge, $x<1$
The diagram below shows the maclaurin series $\ln (1+x)$ expanded to $x^n$, the red dotted lines are is the maclaurin series (with n being the amount of data) and the solid black lines is the main function.
However, when x>1, the red dotted lines look like this, it starts to diverge, why is this the case?
