2乘5分之1+5乘8分之1+到98乘101分之1

因为1/[n(n+3)]=1/3× [1/n-1/(n+3)]所以 1/(2×5)+1/(5×8)+……+1/(98×101)=1/3×(1/2-1/5)+1/3×(1/5-1/8)+……+1/3×(1/98×1/101)=1/3×(1/2-1/5+1/5-1/8+……+1/98-1/101)=1/3×（1/2-1/101）=1/3×99/202=33...