T can be approximated by using the following infinite series:+-+...)Write a program that prints out two versions of the approximation one that goes out to adenominator of 13 and one that goes out of a denominator of 15.T=413 5 7 9Note you will want to use 1.0 for your numerators. In my code I used a decimal version for all ofthese integers.

Start with two variables:pi_approximation initialized to 0, which will store the running…

Answered: can be approximated by using the…

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

Section: Chapter Questions

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T can be approximated by using the following infinite series:
+-+...)
Write a program that prints out two versions of the approximation one that goes out to a
denominator of 13 and one that goes out of a denominator of 15.
T=4
1
3 5 7 9
Note you will want to use 1.0 for your numerators. In my code I used a decimal version for all of
these integers.

Expert Solution

Step 1: Algorithm for Approximating π

Start with two variables:

pi_approximation initialized to 0, which will store the running approximation of π.
sign initialized to 1, which alternates between 1 and -1 to switch the signs in the series.

For each i in the range from 1 to denominator (inclusive) with a step size of 2 (to consider only odd denominators): a. Add sign * (1.0 / i) to pi_approximation. This updates the approximation according to the series formula. b. Toggle the sign by multiplying sign by -1. This alternates the sign for the next iteration.
Multiply pi_approximation by 4 to obtain the final approximation of π.
Return the value of 4 * pi_approximation as the result of the approximation.
Calculate two approximations using this algorithm:

pi_approximation_13 by calling approximate_pi(denominator_13) with denominator_13 as 13.
pi_approximation_15 by calling approximate_pi(denominator_15) with denominator_15 as 15.

Print the results with their respective denominators:

"Approximation with denominator 13: {pi_approximation_13}"
"Approximation with denominator 15: {pi_approximation_15}"

This algorithm uses a loop to calculate the approximation of π using the given infinite series formula and then prints the results for two different denominators.

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