已知字母a,b满足√(a-1)+√(b-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：神马作文网作业帮分类：数学作业时间：2024/11/10 19:01:47

已知字母a,b满足√(a-1)+√(b-2)=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+1/(a+3)(b+3)…+1/(a+2014)(b+201
已知字母a,b满足√(a-1)+√(b-2)=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+1/(a+3)(b+3)+1/(a+4)(b+4)+1/(a+5)(b+5)+1/(a+6)(b+6)+1/(a+7)(b+7)+1/(a+8)(b+8)+1/(a+9)(b+9)+1/(a+10)(b+10)+1/(a+11)(b+11)+1/(a+12)(b+12)+1/(a+13)(b+13)+1/(a+14)(b+14)+…+1/(a+1996)(b+1996)+1/(a+1997)(b+1997)+1/(a+1998)(b+1998)+1/(a+1999)(b+1999)+1/(a+2000)(b+2000)+1/(a+2001)(b+2001)+1/(a+2002)(b+2002)+1/(a+2003)(b+2003)+1/(a+2004)(b+2004)+1/(a+2005)(b+2005)+1/(a+2006)(b+2006)+1/(a+2007)(b+2007)+1/(a+2008)(b+2008)+1/(a+2009)(b+2009)+1/(a+2010)(b+2010)+1/(a+2011)(b+2011)+1/(a+2012)(b+2012)+1/(a+2013)(b+2013)+1/(a+2014)(b+2014)

第一个条件说明 a为1 b为2,然后变成1/1*2+1/2*3+.+1/2015+2016
1/1*2又等于1-1/2,1/2*3等于1/2-1/3
原式变成1-1/2+1/2-1/3+.+1/2015-1/2016
加减消掉最后结果是1-1/2016=2015/2016
应该对的

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