You will write a program that approximates the value of the mathematical constant pi from the following infinite series. π = 4 − 1 + ¼ − ¾¼ + ¼ − 1 + 5 9 Your program will prompt the number of terms in the series to use for the estimate. It will then approximate pi using exactly that many terms. To measure the approximation error, the program will also compute the difference between the approximation and the value of math.pi from the math module. The output for both floating point values should be formatted to 10 decimal places. When your program is run for 6 terms the output should be: Number of terms:6 Estimate of pi: 2.9760461760 Error: 0.1655464775 When your program is run for 99 terms the output should be: Number of terms:99 Estimate of pi: 3.1516934061 Error: -0.0101007525

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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You will write a program that approximates the value of the mathematical constant pi from the following infinite
series.
π =
4
4 1 + 1 - 1 + 1 - + ···
9
11
Your program will prompt the number of terms in the series to use for the estimate. It will then approximate pi using
exactly that many terms. To measure the approximation error, the program will also compute the difference between
the approximation and the value of math.pi from the math module. The output for both floating point values should
be formatted to 10 decimal places.
When your program is run for 6 terms the output should be:
Number of terms:6
Estimate of pi: 2.9760461760
Error: 0.1655464775
When your program is run for 99 terms the output should be:
Number of terms:99
Estimate of pi: 3.1516934061
Error: -0.0101007525
Save and submit your program to Gradescope as pi.py
Transcribed Image Text:You will write a program that approximates the value of the mathematical constant pi from the following infinite series. π = 4 4 1 + 1 - 1 + 1 - + ··· 9 11 Your program will prompt the number of terms in the series to use for the estimate. It will then approximate pi using exactly that many terms. To measure the approximation error, the program will also compute the difference between the approximation and the value of math.pi from the math module. The output for both floating point values should be formatted to 10 decimal places. When your program is run for 6 terms the output should be: Number of terms:6 Estimate of pi: 2.9760461760 Error: 0.1655464775 When your program is run for 99 terms the output should be: Number of terms:99 Estimate of pi: 3.1516934061 Error: -0.0101007525 Save and submit your program to Gradescope as pi.py
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