# Using power series remainder term

## Homework Statement

(For power series about x=1) Using the error formula, show that $$\left|ln(1.5)-p_{3}(1.5)\right|\leq\frac{(0.5)^{4}}{4}$$

## Homework Equations

$$p_{3}(x) = x-1 - \frac{(x-1)^{2}}{2} + \frac{(x-1)^{3}}{3}$$
$$\\\epsilon_{n}(x)=\frac{f^{n+1}(\xi)}{(n+1)!}(x-x_{o})^{n+1}\\where \xi lies between x_{o} and x$$

## The Attempt at a Solution

Im sure this is an easy one, but I cant think of any useful relationship between the difference |f(x)-p_3(x)| and that piece of the remainder function... any hints?
(excuse my latex crappiness)