How many terms of the MacLaurin series for ln(1+x) do you need to use to estimate ln(1.4) to within 0.001?

Question

anonymous · Answer

$$\sum_{n=0}^\infty (-1)^n \frac{x^{n+1}}{n+1}$$

turingtest · Answer

I don't really understand the method for these problems since I have never encountered them before
I would just do trial and error, but I doubt that is what they want

anonymous · Answer

sorry @experimentX  I was not convinced

experimentx · Answer

no it's all right ... besides that was not the correct procedure.

experimentx · Answer

still i think ln(1.4) = ln(1 + 0.4) and the expansion should be as http://home.scarlet.be/math/taylor.htm#ln(1+x)-and-its-Macl

anonymous · Answer

There is a problem quite similiar in my book. It reads "For what values of x is this approximation accurate to within 0.00005"....should I just mimic that example or is the question still too different

turingtest · Answer

they sound the same to me

anonymous · Answer

oh and it's an alternating series...lets see what we have here...

turingtest · Answer

no wait, "values of x" ?
that may change things.... actually I don't understand that idea

experimentx · Answer

i think it would also depend on n, ... if you want it in n=1, then we have to approximate x =  very close to 0.00001

anonymous · Answer

My book calls it the Alternating Series Estimation Theorem?

experimentx · Answer

lol ... i haven't had my lessons for long time. let me check on google

anonymous · Answer

Looks like patrickJMT has a video on it. I'll watch that and see if it helps ;P

experimentx · Answer

http://www.cosmolearning.com/video-lectures/alternating-series-estimation-theorem/ well ... i guess it helps!!