展开全部
1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6+1/5*6*7+1/6*7*8+1/7*8*9+1/8*9*10+1/9*10*11
=(1/2)[(1/1*2)-(1/2*3)]+(1/2)[(1/2*3)-(1/3*4)]+(1/2)[(1/3*4)-(1/4*5)]+...+(1/2)[(1/9*10)-(1/10*11)]
=(1/2)[(1/1*2)-(1/2*3)+(1/2*3)-(1/3*4)+(1/3*4)-(1/4*5)+...+(1/9*10)-(1/10*11)]
=(1/2)[(1/1*2)-(1/10*11)]
=(1/2)(1-1/2-1/10+1/11)
=(1/2)(2/5+1/11)
=(1/2)(27/55)
=27/110.
=(1/2)[(1/1*2)-(1/2*3)]+(1/2)[(1/2*3)-(1/3*4)]+(1/2)[(1/3*4)-(1/4*5)]+...+(1/2)[(1/9*10)-(1/10*11)]
=(1/2)[(1/1*2)-(1/2*3)+(1/2*3)-(1/3*4)+(1/3*4)-(1/4*5)+...+(1/9*10)-(1/10*11)]
=(1/2)[(1/1*2)-(1/10*11)]
=(1/2)(1-1/2-1/10+1/11)
=(1/2)(2/5+1/11)
=(1/2)(27/55)
=27/110.
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