Answered Essay: 1. Introduction In this exercise, we will complete several pieces of Python programs that calculate the value of π and compare their performance. 2. Obj

Its should be done it python and i want the whole code (everything in this assignment)
Its one lab problem so please please complete it and give it to me
PYTHON !!
1. Introduction In this exercise, we will complete several pieces of Python programs that calculate the value of π and compare their performance. 2. Objectives The purpose of this assignment is to give you experience in: Using mathematical formulas in Python. Converting mathematical expressions into Python expressions Refreshing knowledge on function and loops in Python. Doing a little bit study on series based π approximation * Note: Before you start, if you are not familiar with i/else statement, for loop, while loop or function in Python, you are recommended to review the sample codes we covered in lecture first 3. Background 3.1. Calculating π using series π is the ratio of a circles circumference to its diameter. From the early old days, mathematicians have been trying different methods to calculate the value of π. Calculating π by using an infinite series is one popular category for π approximation. In this lab assignment, we will be implementing two types of series for calculation, namely,
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1. Introduction In this exercise, we will complete several pieces of Python programs that calculate the value of π and compare their performance. 2. Objectives The purpose of this assignment is to give you experience in: Using mathematical formulas in Python. Converting mathematical expressions into Python expressions Refreshing knowledge on function and loops in Python. Doing a little bit study on series based π approximation * Note: Before you start, if you are not familiar with i/else statement, for loop, while loop or function in Python, you are recommended to review the sample codes we covered in lecture first 3. Background 3.1. Calculating π using series π is the ratio of a circle’s circumference to its diameter. From the early old days, mathematicians have been trying different methods to calculate the value of π. Calculating π by using an infinite series is one popular category for π approximation. In this lab assignment, we will be implementing two types of series for calculation, namely,

Expert Answer

def GregoryLeibniz(n):
    a = 0
    for i in range(n):
        a = a + ((-1) ** (i)) * (1 / (2 * i + 1))
    return a*4

def Nilakantha(n):
    a=0
    k=0
    for i in range(1,2*n,2):
        a=a+(-1)**(k)*4/((i+1)*(i+2)*(i+3))
        k+=1
    return a+3
###################################################################
#############################4.1###################################
n=100
for i in range(n):
    print(i+1,GregoryLeibniz(i+1),Nilakantha(i+1))
####################################################################

#####################################################################
###############################4.2###################################
pi=3.1415927
accuracy=.001
i=0
diff=1
result=0
while diff>accuracy:
    i=i+1
    result1=result
    result=GregoryLeibniz(i)
    diff=abs(result-result1)

print("GregoryLeibniz",i,result)

result=0
diff=1
i=0
while diff>accuracy:
    i=i+1
    result1 = result
    result=Nilakantha(i)
    diff=abs(result-pi)
    diff = abs(result - result1)

print("Nilakantha",i,result)
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