Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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You've been hired by Leibniz Lauders to write a C++ console application that approximates PI.  Use a validation loop to prompt for and get from the user the number of terms to approximate PI to that is at least 1.  Use the following Leibniz formula:

 

       PI approximation = 4 * (1/1 – 1/3 + 1/5 – 1/7 + 1/9 – 1/11 + …)

 

The terms appear within the parentheses in the formula.  A PI approximation to …

 

  • One term is 4 * (1/1) = 4
  • Four terms = 4 * (1/1 – 1/3 + 1/5 – 1/7) = 2.8952380952
  • Seven terms = 4 * (1/1 – 1/3 + 1/5 – 1/7 + 1/9 – 1/11 + 1/13) = 3.2837384837

 

Use a for statement to calculate the approximation.  Within the loop, use condition i % 2 == 0 to determine whether the loop iteration is even or odd.  Format all real numbers to ten decimal places.  Continue to prompt the user for terms until they enter a sentinel value of 99.  Note that your prompt before the sentinel loop and at the end of the loop is a validation loop rather than a simple prompt.  Loop the program five times with increasing values for the number of terms.  What are the results?

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