(1+1⼀2)*(1+1⼀4)*(1+1⼀6)*...*(1+1⼀10)*(1-1⼀5)*...*(1-1⼀9)

2025-01-05 00:27:38
推荐回答(1个)
回答1:

(1+1/2)(1+1/4)(1+1/6)(1+1/8)(1+1/10)×(1-1/3)(1-1/5)(1-1/7)(1-1/9)
= 3/2 * 5/4 * 7/6 * 9/8 * 11/10 * 2/3 * 4/5 * 6/7 * 8/9 ......化简每个括号
= 3/2 * 2/3 * 5/4 * 4/5 * 7/6 * 6/7 * 9/8 * 8/9 * 11/10 ......利用乘法交换率
= (3/2 * 2/3) * (5/4 * 4/5) * (7/6 * 6/7) * (9/8 * 8/9) * 11/10 ......利用乘法结合率
= 1 * 1 * 1 * 1 * 11/10
= 11/10 ----(即1.1)