直线y=-(n+1)/n+2*x+1/n+2令y=0,得x=1/n+1,与x轴交于(1/n+1,0)令x=0,得y=1/n+2,与y轴交于(0,1/n+2)∴与两坐标围成的三角形面积Sn=1/2*1/(n+2)(n+1)=1/2*(n+2)(n+1)∴S1+S2+S3+.+S2012=[1/(2*3)+1/(3*4)+1/(4*5).+1/(2013*2014)]*1/2=[1/2-1/3+1/3-1/4+1/4-1/5.+1/2013-1/2014]*1/2=[1/2-1/2014]1/2=503/2014(“-(n+1)/n+1*x”中分母的那个n+1应该是n+2吧)