学帮网已知：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+2008)(b+2008)的值?
来源：学生作业学帮网 编辑：学帮网 时间：2024/05/14 12:27:45
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+2008)(b+2008)的值?
√（a-1)+│b-2│=0
a-1=b-2=0
a=1 b=2
1／ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2008)(b+2008)
=1/1*2+1/2*3+1/3*4+...+1/2009*2010
=1/1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010
=1-1/2010
=2009/2010
√（a-1)+│b-2│=0
那么有：a-1=0 b-2=0
a=1 b=2
1／ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2008)(b+2008)
=1/1*2+1/2*3+1/3*4+...+1/2009*2010
=1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010
=1-1/2010
=2009/2010