难题——奥数（2）!（1+1/51）*（1-1/51）*（1+1/52）*（1-1/52）*...*（1+1/152）*

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
看得懂吗?

（1+1/51）*（1-1/51）*（1+1/52）*（1-1/52）*...*（1+1/152）*（1-1/152）
=(1+1/51)(1+1/52)(1+1/53)*……(1+1/152)*(1-1/15)(1-1/52)*……*（1-1/152）
=52/51*53/52*54/53*……*153/152*50/51*51/52*52/53*……*151/152
=153/51*50/152
=3*25/76
=75/76