已知-2=a,-1=b,求1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+…+1/(a-2013)(b-2013)的值

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已知-2=a,-1=b,求1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+…+1/(a-2013)(b-2013)的值已知-2=a,-1=b,求1/ab+1/(a-1)(b-1)+1/(

已知-2=a,-1=b,求1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+…+1/(a-2013)(b-2013)的值
已知-2=a,-1=b,求1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+…+1/(a-2013)(b-2013)的值

已知-2=a,-1=b,求1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+…+1/(a-2013)(b-2013)的值
原式=[(1/-2)-(1/-1)]+[(1/-3)-(1/-2)]+[(1/-4)-(1/-3)].+[(1/-2014)-(1/-2013)]+[(1/-2015)-(1/-2014)]
前后抵消后可得:原式=1+(1/-2015)=2014/2015

2014/2015