MATLAB: Approximating Euler’s sum using while loop

while loop

So I have been working on this code that will approximate the Euler's approximation to within .01% of the actual value. It seems that I may be missing something, when the function runs it will only print the 3 terms, and will print .36111— for almost any number. The actual value that I am trying to approximate is pi^2/6. Could anybody take a look at what I am missing
    function ApproxEulers(PercError,exact)
      i=1;
      sum=0;
      Error = 100;
      while Error >= PercError ;
          i=i+1;
          sum = sum + (1/(i^2));
          Error = Error -(100*abs((exact - sum)/exact));
      end
      fprintf('The number of terms: %d \n', i)
      fprintf('The approxamite value: %.8f \n', sum)
      fprintf('The exact value: %.8f \n', exact)
      end

Best Answer

the line
Error = Error -(100*abs((exact - sum)/exact));
is wrong.
Replace it with
Error = 100*abs((exact - sum)/exact);
also you initialize i to 1, should be 0.
In the end :
function ApproxEulers(PercError,exact)
i=0;
sum=0;
Error = 100;
while Error >= PercError ;
    i=i+1;
    sum = sum + (1/(i^2));
    Error = 100*abs((exact - sum)/exact);
end
fprintf('\n\tThe number of terms: %d \n', i)
fprintf('\tThe approxamite value: %.8f \n', sum)
fprintf('\tThe exact value: %.8f \n\n', exact)
end
which will give you
>> ApproxEulers(.001,pi^2/6)
  The number of terms: 60793 
  The approxamite value: 1.64491762 
  The exact value: 1.64493407
One remark : sum and error are the names of basic matlab functions. try to not use them when you code. Just pick other names to define your variables, otherwise, one day you're gonne struggle to debug a code because of that kind of mistake.
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