Chapter 5.2, Problem 119E

Each of the following infinite series converges to the given multiple of $\pi$or $1/\pi$ .

In each case, find the minimum value of N such that the Nth partial sum of the series accurately approximates the left-hand side to the given number of decimal places, and

give the desired approximate value. Up to place, $\pi$= 3.14 1592653589793....

119. $\left[\text{T}\right]\frac{9801}{2\pi }=\frac{4}{9801}{\displaystyle \underset{k=0}{\overset{\infty }{\sum }}\frac{\left(4k\right)!\left(1303+26390k\right)}{\left(3k\right)!\left(k!\right){640320}^{3k+3/2}},\text{error}}<{10}^{-15}$