For what values of x is the approximate formula: ln(1 + x) = x - (1/2)(x^2) correct to 3 decimal places?
so i know that this is basically the maclaurin series representation of ln(1 + x) since a = 0. i used the convergence test for alternating series and confirmed that this series is indeed converging. so therefore i use the formula for the remainder which is Rn < |a_(n+1)|.
so the first term of the series omited is (1/3)x^3, so |x^3| / 3 should be less than .001 right? since you want the error to be within 3 decimal places. but in my book, they did |x^3| / 3 < .0005. how did they get that?