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In this paper we introduce the so-called truncated very-well-poised$_6\psi_6$ series and set up an explicit recurrence relation for it by means ofthe classical Abel lemma on summation by parts. This new recurrence relationimplies an elementary proof of Bailey's  well-known $_6\psi_6$ summation formula.

A new recurrence relation for the truncated very-well-poised $_6\psi_6$ series and Bailey's summation formula