The Maclaurin series for the arctangent function converges for 1 < x 1 and is given by
Chapter 1, Problem 3(choose chapter or problem)
The Maclaurin series for the arctangent function converges for 1 < x 1 and is given by arctan x = lim n Pn(x) = lim n n i=1 (1) i+1 x2i1 2i 1 . a. Use the fact that tan /4 = 1 to determine the number of n terms of the series that need to be summed to ensure that |4Pn(1) | < 103. b. The C++ programming language requires the value of to be within 1010. How many terms of the series would we need to sum to obtain this degree of accuracy?
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