(1-1/4）1-1/9括号1-1/16省略号括号1-1/百

Question

(1-1/4）1-1/9括号1-1/16省略号括号1-1/百

Answer 1

根据平方差公式，
原式 = (1-1/2)(1+1/2) * (1-1/3)(1+1/3) * (1-1/4)(1+1/4) *......*(1-1/100)(1+1/100)
= 1/2*3/2*2/3*4/3*3/4*5/4*......*99/100*101/100
= 1/2*101/100
= 101/200追问

原式是(1-1/4)(1-1/9)(1-1/16)……(1-1/100)

追答

对啊！
1-1/4 = (1-1/2)(1+1/2)
1-1/9=(1-1/3)(1+1/3)
......
1-1/100=(1-1/10)(1+1/10)
原式= (1-1/2)(1+1/2) * (1-1/3)(1+1/3) * (1-1/4)(1+1/4) *......*(1-1/10)(1+1/10)
= 1/2*3/2*2/3*4/3*3/4*5/4*......*9/10*11/10
= 1/2*11/10
= 11/20