1/8+1/15+1/24+1/35+1/48+1/63+1/80+1/99+1/120+1/143
＝1/2×（1/2-1/4）+1/2×(1/3-1/5)+1/2×(1/4-1/6)+1/2×（1/5-1/7）+1/2×（1/6-1/8）+1/2×（1/7-1/9）+1/2×（1/8-1/10）+1/2×（1/9-1/11）+1/2×(1/10-1/12)+1/2×（1/11-1/13）
＝1/2×(1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8+1/7-1/9+1/8-1/10+1/9-1/11+1/10-1/12+1/11-1/13)
＝1/2×（1/2+1/3-1/12-1/13）
＝1/2×（78/156+52/156-13/156-12/156）
＝1/2×35/52
＝35/104
20062007*2006-20062006*2007+20062006
=20062007*2006-20062006*(2006+1)+20062006
=20062007*2006-20062006*2006
=2006*(20062007-20062006)
=2006
2^2/1*3+3^2/2*4+4^2/3*5+.+99^2/98*100
=(1+1/1*3)+(1+1/2*4)+(1+1/3*5).+(1+1/98*100)
=1*98+(1/1*3+1/3*5+1/5*7+……+1/97*99)+(1/2*4+1/4*6+1/6*8+……+1/98*100)
=98+1/2*(1+1/3-1/5+1/5-1/7+……+1/97-1/99)+1/2*(1/2-1/4+1/4-1/6+1/6-1/8+……+1/98-1/100)
=98+1/2*(1-1/99+1/2-1/100)
=98+1/2*（9900+4950-100-99）
=98+14651/19800