Task 4 [Computing Pl via Leibniz series]This task is to help you use for-loops for mathematical expressions in code.It is an irrational number - that means it cannot be expressed as a fraction. Ever wonder how we compute ?One of the pioneers of the mechanical calculator, Gottfried Wilhelm von Leibniz, proved that could beexpressed with the following infinite series:1-1 1 15 7 9 11 13 15 17 191 1 1 1 1 1++3We can rewrite Leibniz's series in a more compact form asfollows:π = 4 xNotice the alternating plus/minus sign in the series. We call each of the fractions in the series a "term." Tocompute requires the summing of an infinite number of terms; however, in practice, this is not possible.Instead, we can only approximate the true value using a finite number of terms. Using the Leibniz formula, themore terms we compute in the series, the more accurate our calculation of . Your task is to compute π upto a user-specified number of terms (i.e., up to M terms).Don't get scared of math, it is easy once you understand it.The Σ (sigma) symbol is a mathematician's way ofexpressing a "for loop" for summing up terms. Thissymbol means the following:sum=0for nMΣn=0(-1)"2n + 1Your task should work as follows:(1) Ask the user for the number of terms, M.(2) Compute pi based on Leibniz formulation.(3) At each iteration of your for-loop, print out the result(i.e., your current sum x 4)Print your results with precision 12.Compare your result with 3.14159265359.See example output below:our pi= 3.33968253968real pi= 3.14159265359n=5---- Task 4: Compute PIInput number of terms, M: 10n=0adding fraction: 1/1our pi4.00000000000real pi= 3.14159265359n=1adding fraction: -1/3our pi 2.66666666667real pi= 3.14159265359n=2adding fraction: 1/5our pi= 3.46666666667real pi= 3.14159265359n=3our pi 2.89523809524real pi= 3.14159265359n=4adding fraction: -1/7adding fraction: 1/9adding fraction: -1/11our pi 2.97604617605real pi= 3.14159265359n=6adding fraction: 1/13our pi= 3.28373848374real pi= 3.14159265359+ ...=sumrange (0,M+1):sum + [term]Here, [term] is the result of the expression inblue, evaluated using the current value of n in thefor loop. For example, if M=2, we have:TT4n=0, we haven=1, we have(-1)⁰2*0+1(-1)¹2+112*1+1(-1)²n=2, we have2*2+14+1(Look familiar? This is Leibniz's series.)3- +15 n=7adding fraction: -1/153.01707181707= 3.14159265359.. adding fraction: 1/17= 3.25236593472= 3.14159265359our pireal pin=8=our pireal pin=9 ... adding fraction: -1/19our pireal pi3.04183961893= 3.14159265359=n=10 ... adding fraction: 1/21our pi= 3.23231580941real pi = 3.14159265359Try this for M=10000. Remember, before computers, a person would have computed this by hand.Isaac Newton (not using the method above) computed up to a precision of 16 decimal places in 1665.The current record holder is Emma Haruka Iwao. She has estimated with over 31 trillion digits (and not byhand!)

To calculate the value of PI using Lebniz formulation.

Task 4 [Computing Pl via Leibniz series] This task is to help you use for-loops for mathematical expressions in code. It is an irrational number that means it cannot be expressed as a fraction. Ever wonder how we compute ? One of the pioneers of the mechanical calculator, Gottfried Wilhelm von Leibniz, proved that could be expressed with the following infinite series: 1 1 1 1 1 1 1 + + 35-7 1 1 1 + 9 11 13 15 17 19 TT 4 Notice the alternating plus/minus sign in the series. We call each of the fractions in the series a "term." To compute π requires the summing of an infinite number of terms; however, in practice, this is not possible. Instead, we can only approximate the true value using a finite number of terms. Using the Leibniz formula, the more terms we compute in the series, the more accurate our calculation of π. Your task is to compute π up to a user-specified number of terms (i.e., up to M terms). Don't get scared of math, it is easy once you understand it. The Σ (sigma) symbol is a mathematician's way of We can rewrite Leibniz's series in a more compact form as

Task 4 [Computing Pl via Leibniz series] This task is to help you use for-loops for mathematical expressions in code. It is an irrational number that means it cannot be expressed as a fraction. Ever wonder how we compute ? One of the pioneers of the mechanical calculator, Gottfried Wilhelm von Leibniz, proved that could be expressed with the following infinite series: 1 1 1 1 1 1 1 + + 35-7 1 1 1 + 9 11 13 15 17 19 TT 4 Notice the alternating plus/minus sign in the series. We call each of the fractions in the series a "term." To compute π requires the summing of an infinite number of terms; however, in practice, this is not possible. Instead, we can only approximate the true value using a finite number of terms. Using the Leibniz formula, the more terms we compute in the series, the more accurate our calculation of π. Your task is to compute π up to a user-specified number of terms (i.e., up to M terms). Don't get scared of math, it is easy once you understand it. The Σ (sigma) symbol is a mathematician's way of We can rewrite Leibniz's series in a more compact form as

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 6PE

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