1/(2×4)+1/(4×6)+.+1/(2008×2010)=(1/2)[(1/2-1/4)+(1/4-1/6)+(1/6-1/8)……(1/2006-1/2008)+(1/2008-1/2010)]=(1/2)[1/2+(-1/4+1/4)+(-1/6+1/6)+(-1/8+1/8)……+(-1/2006+1/2006)+(-1/2008+1/2008)-1/2010)]=(1/...