1. ## Alternating Series Remainder

Hey Guys,

I have a really quick question about the alternating series remainder.
My teacher gave us this other "theorem" that went along the lines of "accurate to x decimal places" if the remainder was less than $0.5 \times 10^{-x}$

If anyone can correct me on that, it would be greatly appreciated.

TJ

2. Originally Posted by thejinx0r
Hey Guys,

I have a really quick question about the alternating series remainder.
My teacher gave us this other "theorem" that went along the lines of "accurate to x decimal places" if the remainder was less than $0.5 \times 10^{-x}$

If anyone can correct me on that, it would be greatly appreciated.

TJ
Well, I believe what (s)he is referring to is the maximum amount of error that you can expect to encounter if you just use a certain amount of terms in an infinite alternating series. So, from my experiences this last semester, the maximum amount of error you would encounter is less than or equal to the first unused term. Does that kind of answer your question? I'm not so sure about the .5 x 10^-x ...

3. No, it doesn't help.
It's more like, if you want your answer to be accurate to x-decimals, then your remainder has to be less then 0.5x10^(-x).
Something a long those lines.

For the alternating series, not so important.

Say for Lagranges's Remainder. (The AST one was ok)
The actual question is:
How many terms of the Maclaurin series for e^x are needed to approximate $\sqrt{e}$ correct to 2 decimals?

Justify Clearly.
So when using Lagrange's Remainder, I have to put that value in there.
The bad part is I lost my first notebook, which is when we did series... :S

Edit:
I meant Lagrange's, not Taylor's for those who read it before the edit