Question

数学小问题

已知√a-1+(ab-2)²=0，求1/ab+1/(a+1)(b+1）+……+1/（a+2010)(b+2010)

Answer 1

√a-1+(ab-2)²=0
a-1=0,ab-2=0
a=1,b=2
1/ab+1/(a+1)(b+1）+……+1/（a+2010)(b+2010)
=1/(1x2)+1/(2x3)+1/(3x4)+……+1/(2011x2012)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2011-1/2012
=1-1/2012
=2011/2012

Answer 2

由已知a=1，b=2。
所求=1/(1*2)+1(2*3)+...+1/(2011*2012)
=1-1/2+1/2-1/3+...+1/2011-1/2012
=1-1/2012
=2011/2012。