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In QTF theory book of Peskin&Schroder they say:Call 1PI the one particle irreducible diagram,so Fourier two-point correlation function can write:

i/(gamma(vector).p-m0) +i/(gamma.p-m0)(1PI/(gamma.p-m0) +i/(gamma.p-m0)square(1PI/(gamma.p-m0))........=i/(gamma.p-m0-1PI).

They say that we can sum the left hand side to have the right hand side because the left is a geometric serie.But I dont understand why we can sum while we dont know 1PI/(gamma.p-m0) being smaller than 1 or not.Another worrying is that the calculation is done before the making renormalization and QED being asymtotic theory.

Thank you very much in advanced.