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We study a connection between Euler-MacLaurin Summation and Boole Summation suggested in an AMM note from 1960, which explains them as two cases of a general approach to approximation. Herein we give details and extensions of this idea.doi:10.1080/00029890.2009.11920954 fatcat:if457n64cjhnfhjwdpgn4cy7du