I have a power series $$\sum\limits_{n=0}^\infty\frac{(-1)^n}{n+1}\cdot x^{2n+2}$$ and I need to find the interval of convergence. I'm not sure if I did this correctly.
I said the interval of convergence is $[-1, 1]$. I found the radius of the power series to be one after using the ratio test on the power series which resulted in $|x^2| < 1$ for convergence and $|x^2| > 1$ for divergence. Then I just tested the end points and found that both -1 and 1 converged. Is that correct? Thanks.