//Example (pg no.20)

   //the number %pi/4 is the value of infinite series 
//sum(((-1)^i)/(2*i+1))=1-sum(2/(16*(j)^2)-1)
  // The sequence alpha1,alpha2,........is monotone-decreasing
  // to its limit %pi/4
  //  0< =(alpha)n - %pi/4 <= (1/(4*n+3))   n=1,2,.....
  // To calculate %pi/4 correct to within 10^(-6) using this sequence 
  // we would need 10^(6)<=4*n+3
  n=(10^(6)-3)/4
       // roughly n=250,000