Question: In this project, we estimate much more effectively by using the arc tangent series and the relation4=4arctan(15)-arctan(1239)Note that 4=arctan(1)=1-1315-1719 cdots converges too slowly for computational

In this project, we estimate much more effectively by using the arc tangent series and the relation4=4arctan(15)-arctan(1239)Note that 4=arctan(1)=1-1315-1719 cdots converges too slowly for computational purposes.(a) Calculate the Taylor series for arctan(x) centred at 0 and determine its radius of convergence.(b) Show that4=4arctan(15)-arctan(1239)using the following addition formula: if|arctan(x)arctan(y)|<2 then arctan(x)arctan(y)=arctan(xy1-xy)Hint: what is tan(2arctan(15))? what is tan(4arctan(15))? How about tan(4arctan(15)-arctan(1239))?(c) Using the preceding two parts, find a power series formula for 4.(d) Estimate with a finite sum such the the error is within 10-6 by using part (c). Justify your answer.

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