Re: First Year Uni Calculus Marathon
\frac{1}{1+x} = \frac{1}{1 - (-x)} = \sum_{n=0}^{\infty} (-x)^n\\\frac{1}{1+x^2} = \sum_{n=0}^{\infty} (-x^2)^n\\ \int_{0}^{x} \frac{1}{1+t^2}\,dt = \int_{0}^{x} \sum_{n=0}^{\infty} (-1)^nt^{2n}\,dt\\\arctan{x} = \sum_{n=0}^{\infty}\frac{(-1)^n...