作业帮(1+1/2)×(1-1/2)×(1+1/3)×(1-1/3)×……×(1+1/100)×(1-1/100)
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/29 11:57:23
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(1+1/2)×(1-1/2)×(1+1/3)×(1-1/3)×……×(1+1/100)×(1-1/100)
(1+1/2)×(1-1/2)×(1+1/3)×(1-1/3)×……×(1+1/100)×(1-1/100)
(1+1/2)×(1-1/2)×(1+1/3)×(1-1/3)×……×(1+1/100)×(1-1/100)
答案：=3/2 x 1/2 x 4/3 x 2/3 x 5/4 x 3/4 x…x 101/100 x 99/100=3/2 x 4/3 x 5/4 x…x 101/100 x 1/2 x 2/3 x 3/4 x…x 99/100=101/2 x1/100=101/200
将加的相乘 再乘以 减的相乘
(1+1/2)(1+1/3)(1+1/4)……(1+1/100)×(1-1/2)(1-1/3)(1-1/4)……(1-1/100)
=3/2*4/3*5/4……101/100×1/2*2/3*3/4*……*99/100
=101/2×1/100
=101/200