你好像分子、分母都写反了啊.
(1-1/2^2)(1-1/3^2)...(1-1/2010^2)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)...(1+1/2010)(1-1/2010)
=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)...(2008/2009)(2010/2009)(2009/2010)(2011/2010)
=(1/2)(2011/2010)
=2011/4020
100^2/(252^2-248^2)
=100^2/[(252+248)(252-248)]
=100^2/(500×4)
=100×100/(100×20)
=100/20
=5
如果是(252^2-248^2)/100^2
(252^2-248^2)/100^2
=[(252+248)(252-248)]/100^2
=(500×4)/100^2
=100×20/(100×100)
=20/100
=1/5