Question

一道数学题目，大家帮帮忙啊

RT，急啊，(1/2-1)(1/3-1)(1/4-1)(1/5-1)(1/6-1)(1/7-1)(1/8-1)(1/9-1)，大家教教呗。顺便解答，(1/2-1)(1/3-1) =? (1/2-1)(1/3-1)(1/4-1)=? (1/2-1)(1/3-1)(1/4-1)(1/5-1)=?

Answer 1

(1/2-1)(1/3-1)(1/4-1)(1/5-1)(1/6-1)(1/7-1)(1/8-1)(1/9-1)，次式子中八个小括号，每个小括号里的值都是负，偶数个负数相乘得正，所以次式可写为
(每个括号都提个负号出来，被减数与减数交换，8个负号相乘刚好得正)
(1-1/2)(1-1/3)(1-1/4)(1-1/5)(1-1/6)(1-1/7)(1-1/8)(1-1/9/)
=1/2*2/3*3/4*4/5*5/6*6/7*7/8*8/9(约分)
=1/9
2,
(1/2-1)(1/3-1)
=-(1-1/2)*[-(1-1/3)]
=1/2*2/3
=1/3
3,
(1/2-1)(1/3-1)(1/4-1)
方法一同上
方法2：
=(-1/2)*(-2/3)*(-3/4)
=-1/4
4, (1/2-1)(1/3-1)(1/4-1)(1/5-1)
=1/2*2/3*3/4*4/5
=1/5

Answer 2

(1/2-1)(1/3-1)(1/4-1)(1/5-1)(1/6-1)(1/7-1)(1/8-1)(1/9-1)
=(-1/2)*(-2/3)*(-3/4)*...*(-8/9)
=1/9

Answer 3

原式=（1-1/2)……（1-1/9)=1/9
1/3
1/4
1/5

Answer 4

(1/2-1)(1/3-1)(1，(1/2-1)(1/3-1)(1/4-1)(1/5-1)(1/6-1)(1/7-1)(1/8-1)(1/9-1)，
=-1/2*-2/3*......*-8/9=-1/9
(1/2-1)(1/3-1) =1/3
(1/2-1)(1/3-1)(1/4-1)=-1/4
(1/2-1)(1/3-1)(1/4-1)(1/5-1)=1/5