51问答网 > (1-1⼀4)*(1-1⼀9)*(1-1⼀16). . .(1-1⼀81)*(1-1⼀100)等于多少？急求！！！

(1-1⼀4)(1-1⼀9)(1-1⼀16). . .(1-1⼀81)*(1-1⼀100)等于多少？急求！！！

是我们初一数学基训上的智慧园！！本人分数不高

2024-12-20 15:59:34

推荐回答（2个）

回答1：

11/20
(1-1/4)=1-(1/2)2 =(1+1/2)(1-1/2) (1-1/9)=1-(1/3)2=(1+1/3)(1-1/3)
(1-1/16)=1-(1/4)2=(1+1/4)(1-1/4)以此类推(1-1/100)=1-(1/10)2=(1+1/10)(1-1/10)
即3/2*1/2*3/4*2/3*5/4*3/4*6/5*4/5*7/6*5/6*8/7*6/7*9/8*7/8*10/9*8/9*11/10*9/10
中间很多数都可以约分约掉最后就只剩下1/2和11/10 他们两个相乘便可得到最后答案11/20

回答2：

n^2 表示 n的平方.
= = = = = = = = =

解：因为 1 -(1/n)^2 = (1 -1/n) (1 +1/n)
= [ (n-1)/n ] *[ (n+1)/n ],
(n>=2),
所以原式= (1/2) (3/2) (2/3) (4/3) (3/4) (5/4) ... (9/10) (11/10)
= 11/20.

= = = = = = = = =
分解因式：
a^2 -b^2 =(a+b)(a-b).