Why QFT is asymptotic theory but still being very useful?

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ndung200790
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Please teach me this:
Why perturbative QFT is still very useful theory?.Because perturbative QFT is asymptotic theory,so in many cases the series do not converge,then the error might be very large.
Thank you very much for your kind helping.
 
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It seem to me that each Feynman diagram is a possible process.So If our considering includes more and more the diagrams(considering up to higher order terms in the series of perturbation) then our calculation is more and more exactly.But this considering is contrary with asymptotic QFT.(in the asymptotic series,at higher order,then it is the less exactly).So I do not understand where is the reality of the problem.
 
So what is the verification of the ''good'' approximation at low order terms in asymptotic series?Because there is a flaw in the posing the asymptotic series in QFT.
 
It seem that:By perturbation procedure in QFT,the renormalization problem appears.In addition,by the procedure,there are also exist ''compensation things'' appearing among the terms of perturbation series.The compensation values are the cause of the asymptotic characteristic,but at lower order terms of the series,they influence on the terms not much.So at lower order terms,we have a good approximation.Is that correct?