1/[n(n+2)]=[1/n-1/(n+2)]/2
2×4分之1 + 4×6分之1 +……+ 2008x2010分之1
=[1/2-1/4+1/4-1/6+1/6-1/8+.+1/2008-1/2010/]/2
=[1/2-1/2010]/2
=(1005-1)/4020
=251/1005