π can be computed using the following formula: π = 4 x ( 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + . . . ) Write a program that displays the result of  4 x ( 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 ) and 4 x ( 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 +1/13 - 1/15 )

PYTHON PROGRAMMING   (practice review for final) (please see attached)

..5-- I have a python programing question In 1937, a German mathematician named Lothar Collatz formulated an intriguing hypothesis (it still remains unproven) which can be described in the following way: 1. take any non-negative and non-zero integer number and name it c0; 2. if it's even, evaluate a new c0 as c0 ÷ 2; 3. otherwise, if it's odd, evaluate a new c0 as 3 × c0 + 1; 4. if c0 ≠ 1, skip to point 2. The hypothesis says that regardless of the initial value of c0, it will always go to 1. Of course, it's an extremely complex task to use a computer in order to prove the hypothesis for any natural number (it may even need artificial intelligence), but you can use Python to check some individual numbers. Maybe you'll even find the one which would disprove the hypothesis. Write a program which reads one natural number and executes the above steps as long as c0remains different from 1(c0 != 1). Moreover, we'll add another task - we want you to count the steps needed to achieve the goal.…

Justin receives 52 weekly paychecks per year. Each week, he contributes a specific percentage of his gross weekly pay to his retirement plan at work. His employer also contributes to his retirement plan, but at a different rate. Justin wants a program that calculates and displays the total annual contribution made to his retirement plan by him and his employer. Desk-check your solution’s algorithm using $640 as the gross weekly pay, 6% as Justin’s contribution rate, and 4% as the employer’s contribution rate. Then desk-check it using your own set of data.

A polygon is convex if it contains any line segments that connects two points of the polygon. Write a program that prompts the user to enter the number of points in a convex polygon, enter the points clockwise, then displays the area of the polygon. For the formula for computing the area of a polygon,