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I'm approximating $\pi$ using a series in MATLAB. I can approximate to within a relative error of $3\times 10^{-10}$ of MATLAB's built-in value. How would I choose a sensible tolerance for my approximation? Would it possibly relate to machine epsilon?

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    Ok, cool. I'll try that.2011-10-05

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"The usual criterion is to stop when the absolute value of the k-th term is less than the current partial sum times eps"

Thanks to @J.M.