Problem $2(30$ pts$)$

Srinivasa Ramanujan discovered a series formula for $.$

$\frac{1}{}=\frac{2\sqrt[\phantom{2}]{2}}{{99}^2}{\displaystyle \underset{i=0}{\overset{}{}}}\frac{(4i)!}{i{!}^4}\frac{1103+26390i}{{396}^{4i}}$

Write a Python code using just the arithmetic operators $($i$.$e$.,$ no use of any functions or modules$)$ that approximates the value of $$ using the first three terms of the above series. You should find that this approximation is exact up to the first $16$ digits of $.$

Hint: Most problems in math$/$programming can be solved by simply following a series of welldefined instructions. Such instructions constitute an algorithm $($think recipe$).$ To solve this and similar problems, here's a simple algorithm that uses no function calls:

Define a variable for each of the first three terms and assign each variable the Python expression that computes the value

Add the variables

Take the inverse and print the value; this is your output

You must follow this same strategy for solving all the problems in this course. Think of an algorithm to solve the given problem, implement it as a program, and verify the implementation. If you see incorrect results, check the code and$/$or the algorithm for any errors or logical flaws.