Mathematician Leibniz found that * can be approximated by 4 4 4 4 1 +... = 4) (-1)*+1, 11 1 3 7 2 * i – 1 i=1 (a) Write a user-defined function to implement the Leibniz approximation for a by taking n as the input argument and using for loop, wheren is the number of the terms you want to keep in your approximation. (b) Compute the errors in the approximation to a when n = 10, 25, 50, 100. The error is %3D calculated as error = approrimation – n.

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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Mathematician Leibniz found that ī can be approximated by
4
4
1
+
7
+... = 4)(-1)i+1,
11
3
2 * i – 1
i=1
(a) Write a user-defined function to implement the Leibniz approximation for a by taking
n as the input argument and using for loop, wheren is the number of the terms you
want to keep in your approximation.
(b) Compute the errors in the approximation to 7 when n = 10, 25, 50, 100. The error is
calculated as error = approimation – T.
%3D
(c) Write a program in a script file to find out, at least, how many terms needed in the
approximation that the difference between Leibniz approximation and true value n is
within 0.0001, i.e., Jerror| < 0.0001.
Transcribed Image Text:Mathematician Leibniz found that ī can be approximated by 4 4 1 + 7 +... = 4)(-1)i+1, 11 3 2 * i – 1 i=1 (a) Write a user-defined function to implement the Leibniz approximation for a by taking n as the input argument and using for loop, wheren is the number of the terms you want to keep in your approximation. (b) Compute the errors in the approximation to 7 when n = 10, 25, 50, 100. The error is calculated as error = approimation – T. %3D (c) Write a program in a script file to find out, at least, how many terms needed in the approximation that the difference between Leibniz approximation and true value n is within 0.0001, i.e., Jerror| < 0.0001.
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