Over the centuries, people have come up with various ways to approximate the number pi. Here are three infinite series that can be used: Madhava's representation: pi = squareroot 12 sigma^infinity_k=0 (-3)^-k/2k + 1 Newton's: pi = 2 sigma^infinity_k=0 2^k k!^2/(2k + 1)! Ramanujan's: 1/pi = 2 squareroot 2/9801 sigma^infinity_k=0 (4k)! (1103 + 26390k)/(k!)^4 396^4k Do the following: (a) Use the Wikipedia to find when each of the above mathematicians lived. (b) Write script files that sum these series out to the k = 10 term. Find the approximation to pi for each, and compare it to the exact value of pi. How many digits are correct for each? (c) Convert your Newton code to use a while loop instead of a for loop. Use this to determine how many terms must be included in order to approximate pi within 10^-10