I learned about series recently. I noticed a slight similarity between a geometric series $\displaystyle \sum_{n=0}^{\infty} ar^{n} = \frac{a}{1-r}; |r| < 1$

and a integral, say $\displaystyle \int_{a}^{b} \frac{1}{1-x^2}dx$

can you solve using a series instead of trig sub?