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计算1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90的值等于?

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计算1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90的值等于?
计算1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90的值等于?
1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
1/20=1/4-1/5
1/30=1/5-1/6
1/42=1/6-1/7
……
1/90=1/9-1/10
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/9-1/10)
=1-1/10
=9/10