如果有理数理a,b满足|ab-2|+(1-b)2=0试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/22 10:29:51

如果有理数理a,b满足|ab-2|+(1-b)2=0试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2007)(b+2007)的值

写详细步骤有加分么?
易知a=2,b=1
故a-b=1
原失变为:(a-b)/ab + ((a+1)-(b+1))/(a+1)(b+1) +.
=(1/b-1/a)+ (1/(b+1)-1/(a+1)) +.
=(1/b + 1/(b+1) + ...) - (1/a + 1/(a+1) + ...)
把a=b+1代入
原式=1-1/2009=2008/2009

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