Need help on this problem on MATLAB... Calculation of the value of pi. The Nilak

Question

Need help on this problem on MATLAB...

Calculation of the value of pi. The Nilakantha Series was developed in the 15th century as a way to calculate the value of pi pi 3+4/(2*3*4)-4/(4*56)+ 4/(67 8) -4/(8"910)+. Use a for loop to approximate pi using this technique (5 points). Continue the calculations until the absolute value of the difference between the value of pi stored in MATLAB and the approximation is less than 0.001. Report the appproximation and the number of iterations required (5 points). Hint: to alternate the sign on each term use (1) raised to a powerl

Explanation / Answer

% initialize pie to 3

pie = 3;

i = 0;

x = 2;

% infinite loop

while true

   

    % if the error is less than 0.001

    if abs(pie - pi) < 0.001

       

        break;

       

    end

   

   % calculate current term

   temp = 4 / ( x * ( x + 1 ) * ( x + 2 ) );

  

   % if the current term is even term

   if mod( i , 2 ) == 0

      

        pie = pie + temp;

       

   % if the current term is odd term

   else

      

       pie = pie - temp;

      

   end

  

   i = i + 1;

  

   x = x + 2;

   

end

fprintf('Calculate pi : %f ', pie);

fprintf('Actual pi : %f ', pi);

fprintf('No of iterations : %d ', i);

Samle Output

Calculate pi : 3.140881
Actual pi : 3.141593
No of iterations : 6

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