The function $f(x) = \frac{1}{(1+x)}$ has the Maclaurin series:
$$f(x) = \sum_{n=0}^\infty (-x)^n$$ Find the Interval of Convergence
I've gotten to $$\lim_{n\to \infty} \left\lvert \frac{(-x)^{n+1}}{(-x)^n} \right\rvert$$
Unsure where to go from here. I've viewed a few other threads and youtube videos but none seemed to help my case.
Hint: For what values of $r$ can you conclude that $$ \sum_{k=0}^{\infty}r^k=\frac{1}{1-r} $$ edit: this is circular after OP edited in what professor asked.
By the ratio test, which you started doing, you need $$ \lim_{n\rightarrow \infty}|\frac{(-x)^{n+1}}{(-x)^n}|<1\Rightarrow \lim_{n\rightarrow \infty}|-x|<1\Rightarrow |x|<1 $$