- #1

frozenguy

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## Homework Statement

Any problem. Ex Use the Mac series of [tex]tan^{-1}\left(x\right)[/tex] to approximate at [tex]x=\frac{1}{2}[/tex] to three decimal place accuracy.

## Homework Equations

[tex]\sum^{\infty}_{k=0}(-1)^{k}\frac{x^{2k+1}}{2k+1}=x-\frac{x^3}{3}+\frac{x^5}{5}-...[/tex]

## The Attempt at a Solution

I found out using the remainder estimation theorem that all I need is up to the fifth power. So I put x into the expanded series to the fifth power (third term) and then I take three decimal places, rounding the third.

The books answer is four decimal places, fourth rounded and an answer that comes from using the seventh power (fourth term).

So, what am I doing wrong.. I have encountered this on several problems in the book.

Am I using my remainder estimation theorem wrong?

[tex]\frac{\left(\frac{1}{2}\right)^{n+1}}{n+1}<0.0005[/tex]Using my calculator, I find at n=5, the left side is less then 0.0005