Common Maclaurin Series

Good to know to speed up solving. Would recommend using written practice.

$$\frac{1}{1-x}$$

$$\sum_{n=0}^{\infty} x^n; x\in(-1,1)$$

$$e^x$$

$$\sum_{n=0}^{\infty} \frac{x^n}{n!}$$

$$\sin{x}$$

$$\sum_{n=0}^{\infty} \frac{(-1)^{n}x^{2n+1}}{(2n+1)!}$$

$$\cos{x}$$

$$\sum_{n=0}^{\infty} \frac{(-1)^{n}x^{2n}}{(2n)!}$$

$$\arctan{x}$$

$$\sum_{n=0}^{\infty} \frac{(-1)^{n}x^{2n+1}}{2n+1}; x \in [-1,1]$$

$$\ln(1-x)$$

$$\sum_{n=1}^{\infty} -\frac{x^n}{n}; x \in [-1,1)$$

$$\ln(1+x)$$

$$\sum_{n=1}^{\infty} \frac{(-1)^{n+1}x^n}{n}; x \in (-1,1]$$