Calculate the circumference rate by using the Newton series, 15 decimal places after the decimal point, Newton's circumference Rate

Calculate the circumference rate by using the Newton series, 15 decimal places after the decimal point, Newton's circumference Rate

In the 18th century, mathematicians developed a number of Infinite Series for calculating the circumference rate. Among them, Newton studied the following series:

This Infinite Series is used to calculate the circumference rate to 15 digits after the decimal point.

 

Method: perform the following simple deformation on the above formula to conveniently compile the program.

 

 

 1 #include <iostream> 2 #include <iomanip> 3 using namespace std; 4  5 int main( void )    /* name: Pinew.cpp */ 6 {    double s, t, p; 7     int a, b, n; 8     s=3.0;    t=3.0;    a=1;    b=2;    n=0; 9     cout<<fixed<<setprecision(15);10     do11     {   t=0.25*t*a/b;12         p=t/(a+2);13         s+=p;14         n++;15         cout<<"n="<<setw(4)<<n<<"  Pi="<<s<<endl;16         a+=2;17         b+=2;18     }while(p>=1E-18);19     20     return 0;21 }

Running result:

N = 1 Pi = 3.125000000000000
N = 2 Pi = 3.139062500000000
N = 3 Pi = 3.141155133928572
N = 4 Pi = 3.141511172340030
N = 5 Pi = 3.141576715774867
N = 6 Pi = 3.141589425319122
N = 7pi = 3.141591982358383
N = 8 PIOs = 3.141592511157862
N = 9 Pi = 3.141592622870617
N = 10pi = 3.141592646875561
N = 11 Pi = 3.141592652105887
N = 12 Pi = 3.141592653258738
N = 13 Pi = 3.141592653515338
N = 14 Pi = 3.141592653572930
N = 15 Pi = 3.141592653585950
N = 16 Pi = 3.141592653588912
N = 17 Pi = 3.141592653589590
N = 18 Pi = 3.141592653589746
N = 19 Pi = 3.141592653589782
N = 20 PIOs = 3.141592653589790
N = 21 Pi = 3.141592653589792
N = 22 PIOs = 3.141592653589793
N = 23 Pi = 3.141592653589793
N = 24 Pi = 3.141592653589793
N = 25 Pi = 3.141592653589793
N = 26 Pi = 3.141592653589793
N = 27 PIOs = 3.141592653589793