Question

初一数学计算题，请求答题高手解答！！

(1-1/2²)×(1-1/3²)×···×(1-1/9²)×(1-1/10²)

Answer 1

1-1/n^2=(n^2-1)/n^2=(n-1)(n+1)/n^2=(n-1)/n * (n+1)/n
如：(1-1/2²)=1/2 * 3/2
(1-1/3²)=2/3 * 4/3
(1-1/9²)=8/9 *10/9
(1-1/10²)=9/10 * 11/10
可知中间项都消去了，只剩了1/2 与 11/10
所以结果为11/20

Answer 2

1-1/2^2)（1-1/3^2）……（1-1/10^2)
=[(2/2)^2-(1/2)^2][(3/3)^2-(1/3)^2]......[(10/10)^2-(1/10)^2]
=[(1/2)*(3/2)][(2/3)*(4/3)]......[(9/10)*(11/10)]
=(1/2)*(11/10)
=11/20

Answer 3

(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/10)(1+1/10)

=1/2×11/10=11/20

Answer 4

11/20