Is $1+p/2!+p^2/3!+p^3/4!・・・$ convergent in $ \Bbb{Z}_p$?

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Let $p$ be an odd prime.Is $1+p/2!+p^2/3!+p^3/4!・・・$ convergent in $ \Bbb{Z}_p$? I know $1+p+p^2/2!+p^3/3!+・・・$ converges but what about the titled case ?