Nama : Ryo Hadinata
NIM : 1601250023
04PAW
IT-Math
Bina Nusantara University
Case Study:
Write a program that approximates the value of π by summing the terms of this series: 4/1 – 4/3 + 4/5 – 4/7 + 4/9 – 4/11 + …
The program should prompt the user for n, the number of terms to sum, and then output the sum of the first n terms of this series. Have your program subtract the approximation from the value of math.pi to see how accurate it is.
Ans:
import math def function(n): result = ((-1.0)**(n+1)) * (4.0/(2*n-1)) return result def main(): result = 0 n = int(input("Please input n: ")) for x in range(1, n+1): result = result + function(x) print("\n\nResult: ") print("============") print("Value of math.pi = " + str(math.pi)) print("Approximation by program = " + str(result)) print("Math.pi - Approximation = " + str(math.pi - result)) print("True Fractional Relative Error = " + str((math.pi-result)/math.pi)) print("True Percent Relative Error = " + str(((math.pi-result)/math.pi)*100) + "%") main()
Click to download code (*.py)
n = 10
Output:
Please input n: 10 Result: ============ Value of math.pi = 3.14159265359 Approximation by program = 3.04183961893 Math.pi - Approximation = 0.0997530346604 True Fractional Relative Error = 0.0317523771092 True Percent Relative Error = 3.17523771092%