若|a-2|+(b-1)的平方=0 1/ab+1/(a+1)(b+1) + 1/(a+2)(b+2)+...+1/(a+2008)(b+2008)的值
问题描述：
若|a-2|+(b-1)的平方=0 1/ab+1/(a+1)(b+1) + 1/(a+2)(b+2)+...+1/(a+2008)(b+2008)的值
答
你好！
∵|a-2|+(b-1)²=0
∴a-2=0 a=2
b-1=0 b=1
1/(1*2) = 1- 1/2
1/(2*3) = 1/2 - 1/3
1/(3*4)=1/3 -1/4
……
1/(2009*2010) = 1/2009 - 1/2010
∴原式= 1/(1*2) + 1/(2*3) +……+1/(2009*2010)
= 1-1/2+1/2-1/3+……+1/2009-1/2010
=1 - 1/2010
= 2009/2010
答
若|a-2|+(b-1)的平方=0
a-2=0 a=2
b-1=0 b=1
1/(a+1)(b+1) + 1/(a+2)(b+2)+...+1/(a+2008)(b+2008)
=1/3*2+1/4*3+……+1/2010*2009
=1/2-1/3+1/3-1/4+……+1/2009-1/2010
=1/2-1/2010
=502/1005
答
∵|a-2|+(b-1)²＝0∵|a－2|≥0(b-1)²≥0∴a－2＝0 a＝2b－1＝0 b＝1∵a－b＝2－1＝11/(1／2) = 1- 1/21/(2×3) = 1/2 - 1/31/(3*4)=1/3 -1/4……1/(2009×2010) = 1/2009 - 1/2010若1／n﹙n＋1﹚＝1／n－...