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 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 1-1/3+1/5-1/7+... 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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