How can an asymptotic series give accurate results as in QED?

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shunra
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The results of QED calcualtions are in the form of an asymptotic series in the fine structure constant. This means that if one adds too many terms, the result diverges. So what is the meaning of "18 digits accuracy" of certain QED calculations, if they can be spoiled by adding MORE loops to the calculation or LESS ?
 
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In case of an asymptotic series you have to stop adding higher-order terms if these start to become larger than the previous term.
 
Thank you vanhees71.
In the case of QED, is the above "reversal point" also the point where the best agreement with experiment is achieved?