Showing that a certain number is equal to some infinite sum of numbers using power series. For example, showing that $ln(2)=1-\frac{1}{2}+\frac{1}{3}-...$$\ln(2)=1-\frac{1}{2}+\frac{1}{3}-\cdots$ or $e=2+\frac{1}{2}+\frac{1}{3!}+...$$e=2+\frac{1}{2}+\frac{1}{3!}+\cdots$.