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

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

$\sum_{n=1}^{\infty} \frac{f(x) - f(a)}{n}(x - a)^n$

$f(a) + f'(x)(x - a) + f''(x)(x - a)^2 + \cdots$