(1+1/51)*(1-1/51)*(1+1/52)*(1-1/52)*.*(1+1/152)*(1-1/152)

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(1+1/51)*(1-1/51)*(1+1/52)*(1-1/52)*.*(1+1/152)*(1-1/152)
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(1+1/51)*(1-1/51)*(1+1/52)*(1-1/52)*.*(1+1/152)*(1-1/152)
(1+1/51)*(1-1/51)*(1+1/52)*(1-1/52)*.*(1+1/152)*(1-1/152)

(1+1/51)*(1-1/51)*(1+1/52)*(1-1/52)*.*(1+1/152)*(1-1/152)
=(1-1/51)*(1+1/51)*(1-1/52)*(1+1/52)*.*(1-1/152)*(1+1/152)
=(50/51)*(52/51)*(51/52)*(53/52)*.*(151/152)*(153/152)
中间约分
=(50/51)*(153/152)
=75/76

原式=[1-1/(51*51)]*[1-1/(52*52)]*[1-1/(53*53)]*............*[1-1/(152*152)]
=[(51*51-1)/(51*51)]*[(52*52-1)/(52*52)]*[(53*53-1/(53*53)]*............*[(152*152-1)/(152*152)]
=[(50*52)/(51*51)]*[(51*53)/(52*52)]*[(52*54/(53*53)]*............*[(151*153)/(152*152)]
=(50/51)*(153/152)
=75/76

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