已知|ab-2|+(b+1)^2=0 求b^2009-(-a/2)^2009和1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+……+1/(a-2009)(b-2009)

问题描述:

已知|ab-2|+(b+1)^2=0 求b^2009-(-a/2)^2009和1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+……+1/(a-2009)(b-2009)

|ab-2|+(b+1)^2=0
ab-2=0
b+1=0
b=-1
a=-2
b^2009-(-a/2)^2009
=(-1)^2009-(-(-2)/2)^2009
=-1-1
=-2
1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+……+1/(a-2009)(b-2009)
=1/2+1/2*3+1/3*4+...+1/2010*2011
=1-1/2+1/2-1/3+1/3-1/4+...+1/2010-1/2011
=1-1/2011
2010/2011