Let $I\subset\mathbb R$ be an interval and $f:I\to\mathbb R$ be a $(n+1)$ times continuously differentiable function. For any values $a,x\in I,$ the value $f(x)$ can be written as
$$f(x)=f(a)+\sum_{k=1}^n \frac{f^{\{k\}}(a)}{k!}(x-a)^k+R_{n+1}(x)$$ where $k!$ denotes the factorial, $f^{\{k\}}$ denots the $k$-th derivative of $f$ and the remainder term $R_{n+1}$ equals the Riemann integral. $$R_{n+1}(x)=\frac 1{n!}\int_a^x (x-t)^nf^{\{n+1\}}(t)dt.$$
