(1/50-1)*(1/49-1)*(1/48-1)*.*(1/2-1)

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(1/50-1)*(1/49-1)*(1/48-1)*.*(1/2-1)(1/50-1)*(1/49-1)*(1/48-1)*.*(1/2-1)(1/50-1)*(1/49-1)*(1/48-1)*.

(1/50-1)*(1/49-1)*(1/48-1)*.*(1/2-1)
(1/50-1)*(1/49-1)*(1/48-1)*.*(1/2-1)

(1/50-1)*(1/49-1)*(1/48-1)*.*(1/2-1)
1/50-1)(1/49-1)(1/48-1).(1/4-1)(1/3-1)(1/2-1)
= (-1)^49 * (1-1/50)(1-1/49)...(1-1/2)
= (-1) * (49/50)(48/49)...(2/3)(1/2)
= (-1) * (49*48*.*2*1)/(50*49*48*.*3*2)
= (-1) * (1)/(50)
= -1/50

-49/50*48/49*47/48*....1/2
=-1/50

(1/50-1)*(1/49-1)*(1/48-1)*........*(1/2-1)
=-(1-1/50)*(1-1/49)*(1-1/48)*........*(1-1/2)
=-49/50*48/49*47/48*........*2/3*1/2 (内部全部抵消)
=-1/50

(1/50-1)*(1/49-1)*(1/48-1)*........*(1/2-1)
=(-1)^49*(49/50)*(48/49)*(47/48)*……*(1/2)
=-1/50

原式=-(1-1/50)*(1-1/49)*(1-1/48)*........*(1-1/2)
=-49/50*48/49*47/48*........*2/3*1/2 =-1/50