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There are many formulae for computing (the ratio of a circle's circum ference to its diameter). The simplest is =1-1/341/5-1/7+1/9 4 (8.4) which comes from putting x in the series arctan x - x (8.5) 3 579 (a) Write a program to compute using Equation (8.4). Use as many terms in the series as your computer will reasonably allow (stait modestly, with 100 terms, say, and re-run your program with more and more each time). You should find that the series converges very slowly i.e. it takes a lot of terms to get fairly close to (b) Rearranging the series speeds up the convergence 81x 35x7 9 x 11 Write a program to compute using this series instead. You should find that vou need fewer terms to reach the same level of accuracy that you got in (a)