how to calculate alternating summation for pi

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John Jamison 2017-1-31

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https://ww2.mathworks.cn/matlabcentral/answers/322627-how-to-calculate-alternating-summation-for-pi

评论： Star Strider 2017-1-31

How do I write code to estimate pi up to 1 million terms (n=1million) of: pi = 4(1/1 - 1/3 + 1/5 - 1/7 +...etc)

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Answer 1

Star Strider 2017-1-31

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https://ww2.mathworks.cn/matlabcentral/answers/322627-how-to-calculate-alternating-summation-for-pi#answer_252702

在 MATLAB Online 中打开

Use MATLAB vectors:

N = 1E+6;                                               % Number Of Terms
N = 2*fix(N/2);                                         % Assure Even Number Of Terms
sgn = -(-1).^[1:N];                                     % Sign Vector
denom = 1:2:2*N;                                        % Denominator Vector
pie = 4*sum(1./(denom.*sgn))                            % Desired Result
error = pi - pie                                        % Difference Between Our Calculation And MATLAB ‘pi’
pie =
          3.14159165358978
error =
      1.00000001213019e-06

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John Jamison 2017-1-31

for the 'sgn' and 'denom' steps, how could you make those into vector equations—i.e 'v =' ?

Star Strider 2017-1-31

在 MATLAB Online 中打开

I’m not certain what you mean by ‘vector equations—i.e 'v =' ’ A more detailed description or explanation would be helpful.

They are already ‘vector equations’ as I interpret it. I combined them in the ‘pie’ assignment. You can break them out as a single vector and then calculate ‘pie’ as: