September 30th, 2009, 07:52 AM  #1 
Newbie Joined: Jun 2009 Posts: 13 Thanks: 0  error term for arctan(x)
The question reads: Find a vale of n so that any partial sum with at least n terms is within 1/100 of the target value of pi/4 of the series 11/3+1/51/7+... From our book and notes in class this is the arctan series where you let x = y^2. I know that the error term is employed to find n. If my notes are correct then the error terms is the intergral of (y)^n / 1+y^2 dy. (Sorry for not knowing how to format it probably). Another student in my class said that the error term is actually the intergral of y^n dy. Which one is it? Thank you for the help. TomC 
October 22nd, 2009, 08:49 AM  #2 
Newbie Joined: Oct 2009 Posts: 8 Thanks: 0  Re: error term for arctan(x)
if x_1  x_2 + x_3  x_4 + ... is an alternating series (x_i > 0 for all i) with x_i's strictly decreasing, then you can show that the partial sum x_1  x_2 + x_3  x_4 + ... + (1)^(n+1) x_n is within x_n of the limit. No arctan required (of course we're assuming that the problem isn't lying and the limit actually is pi/4). 

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arctanx, error, term 
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