How To Calculate The Value Of PI With A Program?

Writec++program calculate valueof pi from the infinte seriespi=4-4/3+4/5-4/7+4/9 ...print table show valueofpi?

• print table show value of pi approximated by 1 term of this series,by 2 term, 3 term, etc. how many terms of this series do you have to use before you first get 3.14? 3.141? 3.1415? 3.14159

• Answer:

  See below for the basic computation, with minimal output. Even though the algorithm is relatively simple, there's still the opportunity for some elegance in implementation. I wanted to show you a way to do that, in addition to giving a correct result. I'll leave it to you to display a table, if you need it, and add logic to determine when you've reached your estimate milestones. Or, you can just run it interactively and use trial and error to answer the accuracy questions. #include <iostream> #include <sstream> using namespace std; double piEst(unsigned, bool); typedef double (*func)(double,double); double add(double,double); double subtract(double,double); typedef struct { func f[2]; double den; } Op_t; int main(int argc, char *argv[]) { unsigned n; stringstream *ss; if (argc > 1) ss = new stringstream(argv[1]); if ((argc < 2) || (!((*ss) >> n)) || (n < 1)) { cout << "usage : " << argv[0] << " <n>" << endl; cout << " where <n> = number of terms, a positive integer" << endl; return -1; } double pi = piEst(n,false); cout << endl << "number of terms in series = " << n; cout << ", estimated pi = " << pi << endl; } double piEst(unsigned numTerms, bool display) { double num = 4.0; double pi = 0.0; Op_t op; op.f[0] = add; op.f[1] = subtract; op.den = 1.0; for (unsigned i = 0; i < numTerms; i++, op.den += 2.0) { pi = op.f[i%2](pi,num/op.den); if (display == true) cout << pi << endl; } return pi; } double add(double a,double b) { return a + b; } double subtract(double a,double b) { return a - b; }