观察下列等式:1*1/2=1-1/2,2*2/3=2-2/3,3*3/4=3-3/4,……请你计算(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8打错了,是请你计算(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8 x ……x(10-10/11)/1
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![观察下列等式:1*1/2=1-1/2,2*2/3=2-2/3,3*3/4=3-3/4,……请你计算(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8打错了,是请你计算(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8 x ……x(10-10/11)/1](/uploads/image/z/8601271-7-1.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E7%AD%89%E5%BC%8F%EF%BC%9A1%2A1%2F2%3D1-1%2F2%2C2%2A2%2F3%3D2-2%2F3%2C3%2A3%2F4%3D3-3%2F4%2C%E2%80%A6%E2%80%A6%E8%AF%B7%E4%BD%A0%E8%AE%A1%E7%AE%97%EF%BC%881-1%2F2%29%2F10+x+%282-2%2F3%29%2F9+x+%283-3%2F4%29%2F8%E6%89%93%E9%94%99%E4%BA%86%EF%BC%8C%E6%98%AF%E8%AF%B7%E4%BD%A0%E8%AE%A1%E7%AE%97%EF%BC%881-1%2F2%29%2F10+x+%282-2%2F3%29%2F9+x+%283-3%2F4%29%2F8+x+%E2%80%A6%E2%80%A6x%EF%BC%8810-10%2F11%EF%BC%89%2F1)
观察下列等式:1*1/2=1-1/2,2*2/3=2-2/3,3*3/4=3-3/4,……请你计算(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8打错了,是请你计算(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8 x ……x(10-10/11)/1
观察下列等式:1*1/2=1-1/2,2*2/3=2-2/3,3*3/4=3-3/4,……请你计算(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8
打错了,是请你计算(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8 x ……x(10-10/11)/1
观察下列等式:1*1/2=1-1/2,2*2/3=2-2/3,3*3/4=3-3/4,……请你计算(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8打错了,是请你计算(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8 x ……x(10-10/11)/1
关键在于逆应用条件1*1/2=1-1/2,2*2/3=2-2/3,3*3/4=3-3/4,由题意得
(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8 x ……x(10-10/11)/1
=(1x1/2x1/10)x(2x2/3x1/9)x(3x3/4x1/8)x.x(8x8/9x1/3)x(9x9/10x1/2)x(10x10/11x1/1)(整理简化运算)
=(1x2x3x...x10)x(1/10x1/9x1/8x1/7x.x1/2x1/1)x(1/2x2/3x3/4x.x8/9x9/10x10/11)
=1/11
给点分吧!
1/60
算到一半晕了。。。
关键在于逆应用条件1*1/2=1-1/2,2*2/3=2-2/3,3*3/4=3-3/4,由题意得
(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8 x ……x(10-10/11)/1
=(1x1/2x1/10)x(2x2/3x1/9)x(3x3/4x1/8)x....x(8x8/9x1/3)x(9x9/10x1/2)x(10x10/11x1/1)(整理简化运算...
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关键在于逆应用条件1*1/2=1-1/2,2*2/3=2-2/3,3*3/4=3-3/4,由题意得
(1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8 x ……x(10-10/11)/1
=(1x1/2x1/10)x(2x2/3x1/9)x(3x3/4x1/8)x....x(8x8/9x1/3)x(9x9/10x1/2)x(10x10/11x1/1)(整理简化运算)
=(1x2x3x...x10)x(1/10x1/9x1/8x1/7x....x1/2x1/1)x(1/2x2/3x3/4x.....x8/9x9/10x10/11)
=1/11
收起