Objectivo
Desarrollar un programa Python para calcular una aproximación de PI usando la expresión:
pi/4 = 1/1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 ...
El usuario especificará la cantidad de términos que se utilizarán y el programa mostrará todos los resultados hasta esa cantidad de términos.
Ejemplo Ejercicio Python
Mostrar Código Python
# Prompt the user for the number of terms
num_terms = int(input("Enter the number of terms: "))
# Initialize variables
pi_approximation = 0
sign = 1 # This alternates between 1 and -1 for each term
# Loop through the terms to calculate the approximation
for i in range(num_terms):
term = sign / (2 * i + 1) # Calculate the current term
pi_approximation += term # Add the term to the approximation
sign *= -1 # Alternate the sign for the next term
# Multiply the approximation by 4 to get the value of pi
pi_approximation *= 4
# Display the result
print(f"Approximated value of PI using {num_terms} terms: {pi_approximation}")
Output
Case 1:
Enter the number of terms: 5
Approximated value of PI using 5 terms: 3.339682539682539
Case 2:
Enter the number of terms: 10
Approximated value of PI using 10 terms: 3.0418396189294032
Case 3:
Enter the number of terms: 20
Approximated value of PI using 20 terms: 3.121595216925108
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