Question

Write a C++ program using a while loop to calculate the value of pi/2 accurate to 6 digits after the decimal point using the following series:

1+2 1+2+3 ==1+53+5+7

DIsplay the following and turn in printouts of the program and the results:

The number of terms needed to find pi/2

THe value of pi/2 using acos(-1.0)/2 using 10 digits after the deciaml point

The value of pi/2 found with the series using 10 digits after the decimal points (The first 6 digits after the decimal point sohuld match the value above.)

Answer 1

#include <iostream>
#include <cmath>
using namespace std;
const double pi = 3.141592653589793238462643383;//actual value of PI

int main()
{
int num_accuracy=6;//accuracy for 6 digits
double x = 1.0;//initial value of x
int i = 0;//number of terms without counting the first term
double curr = 1.0;
while(1)
{
i++;//increasing number of terms
curr = curr*i/(2*i+1);//summation term for each iteration

x = x + curr;

if(fabs(x-pi/2.0)<pow(10.0,-1*num_accuracy))//checking if value is in error range
break;
else continue;
}
printf("Value of pi upto accurate upto 6 digits: %.12f\n", x);
cout << "Number of terms: " << i+1 << endl;//i+1 by including the first term

double pi_exact = acos(-1.0)/2;//value of pi calculated using acos
printf("Value of pi using acos: %.12f\n", pi_exact);
num_accuracy = 10;//for accuracy upto 10 digits
x = 1.0;
i = 0;
curr = 1.0;
while(1)
{
i++;
curr = curr*i/(2*i+1);

x = x + curr;

if(fabs(x-pi/2.0)<pow(10.0,-1*num_accuracy))//checking if value is in error range
break;
else continue;
}
printf("Value of pi upto accurate upto 6 digits: %.12f\n", x);
cout << "Number of terms: " << i +1<< endl;
}

File Edit Selection Find View Goto Tools Project Preferences Help #include #include <iostream» <cmath> 3 using namespace std; 4 const double pi3.141592653589793238462643383;//actual value of PT int main() int nun accuracy-6;//accuracy for 6 digits double x1.8;//initial value of x int i - 8;//number of terms without counting the first tern double curr-1.e while(1) 18 12 13 i++//increasing number of terns 15 16 17 18 19 2e 21 curr curr*í/(2*1+1);//sunmation term for each İteration x x + curr if(fabs(x-pi/2.0)<pow(18.е,-1+num-accuracy) )//checking if else continue; value is in error range break; 23 24 25 26 27 28 29 3e 31 32 printf("Value of pi upto accurate upto 6 digits: %.12fin", x); cout << "Number of terns: << i+1 << endl;//i+1 by including the first term double pi_exact acos (-1.8)/2;//value of pi calculated using acos printf("Value of pi using acos: %.12fin", pi-exact); nun accuracy 18;//for accuracy upto 18 digits x1.8; curr 1.8; while(1) 34 35 36 37 38 39 48 41 42 43 i++5 curr curr i/(2*i+1); xx curr if(fabs(x-pi/2.8)<pow (18.8,-1*num_accuracy))//checking if value is in error range break; else continue; printf( "Value of pi upto accurate upto 6 digits: %.12fin", x); cout << "Number of terms: " << İ +1<< endl; 45 47 48 Line 48, Column 1 Spaces: 4

Sample output:

.

Value of pi upto accurate upto 6 digits: 1.570795583496 Number of terms:19 alue of pi using acos: 1.570796326795 Value of pi upto accurate upto 6 digits: 1.570796326724 Number of terms:32 Process returned e (exe) Press any key to continue. execution time 0.094 s

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