Is Perturbative Theory Meaningless in Some Cases Despite Small Interaction?

[ndung200790]

Please teach me this:
Because perturbative QTF theory is an asymptotic theory,then when the series is divergent(the terms of series increase as the n(the number of terms) tend to infinite) I wonder whether the theory is meaningfull or meaningless.
Thank you very much in advanced.

 

[Demystifier]

It's meaningful when you take only a few terms of the expansion, but meaningless if you take them all.

 

[ndung200790]

Then,with very large error(despite of taking a few terms in series),why it is still meaningfull?

 

[Demystifier]

Sometimes the error is small, which is why sometimes it's meaningfull.