初一计算题

原式
=[(1×3)/(2×2)]·[(2×4)/(3×3)]·[(3×5)/(4×4)]·.......·[(9×11)/(10×10)]
=[(1/2)×(3/2)]×[(2/3)×(4/3)]×[(3/4)×(5/4)]×........×[(9/10)×(11/10)]
=(1/2)×[(3/2)×(2/3)]×[(4/3)×(3/4)]×[(5/4)×........×(9/10)]×(11/10)
=(1/2)×(11/10)
=11/20

全部用平方差公式化简
(1-1/(2^2))·(1-1/(3^2))·(1-1/(4^2))……(1-1/(10^2))
= (1/2)(3/2)*(2/3)(4/3)*(3/4)(5/4)……(9/10)(11/10)
中间部分可以约掉
= (1/2)*(11/10)
= 11/20

11/20