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2小时内满分题)若√a-1 +√ab-2 =0,求1/ab+1/(a+1)(b-1)+1/(a+2)(b-2)+…+1/

来源:学生作业帮 编辑:作业帮 分类:综合作业 时间:2024/05/13 08:54:44
2小时内满分题)
若√a-1 +√ab-2 =0,求1/ab+1/(a+1)(b-1)+1/(a+2)(b-2)+…+1/(a+2004)(b+2004)的值.
我可以由√a-1 +√ab-2 =0算出a=1 ,ab=2即b=2,但是代入去算就不会!
√a-1 +√ab-2 =0
a=1 ,ab=2即b=2
1/ab+1/(a+1)(b-1)+1/(a+2)(b-2)+…+1/(a+2004)(b+2004)
=1/1*2+1/2*3+1/3*4+...+1/2005*2006
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2005-1/2006)
=1-1/2006
=2005/2006