3 7 13 2008×2009＋1

n×(n+1)+1 1 1 1
————— = 1 + ———— = 1 + —— — ——
n×(n+1) n×(n+1) n n+1
3 7 13 2008×2009＋1
— ＋ — ＋ — ＋……＋————————
2 6 12 2008×2009
=1+1/(1×2)+1+1/(2×3)+1+1/(3×4)+……+1+1/(2008×2009)
=2008+(1/1-1/2+1/2-1/3+1/3-1/4+……+1/2008-1/2009)
=2008+(1-1/2009)
=2008又2009分之2008