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Problem 1 ) The Taylor series expansion of t a n - 1 x for | x | 1 is: t a n - 1

Problem 1) The Taylor series expansion of tan-1x for |x|1 is:
tan-1x=x-x33+x55-cdots=n=0(-1)nx2n+12n+1
Develop an algorithm that performs the following (you can present it in the form of a pseudo-code or a list of steps):
The algorithm determines tan-1x using the above equation, where the argument x is the input, and the output argument y is the approximate value for tan-1x obtained using Taylor's series expansion. If an is the nth term of the series, then sum Sn of the first n terms is Sn=Sn-1+an. In each pass, calculate the estimated error E given by E=|an|. Stop adding terms when E10-9, and report y.
Note: You are not asked to submit any code for this part. Submitting the algorithm is sufficient.
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