Hi all, here's the problem: given: [tex]tan^(-1)= x - x^3/3 + x^5/5[/tex] using the result [tex]tan^(-1) (1)= pi/4[/tex] how many terms of the series are needed to calculate pi to ten places of decimals? note: this is supposed to say tan^(-1) and tan^(-1) respectively Does anyone know whether there's a formula to calculate the accuracy/number of decimals of the Taylor expansion? In my books I found a formula to calculate the approximation of error from the remainder term - not sure, how that would help, though. The above seems to be one of those standard questions that one should definitely be able to solve in order to pass an exam. So, if anyone knows - help's much appreciated!