1/2+5/6+11/12+……+9899/9900
=(1-1/2)+(1-1/6)+(1-1/12)+……+(1-1/9900)
=(1-1/(1*2))+(1-1/(2*3))+(1-1/(3*4))+……+(1-1/(99*100))
=1*99-【1/(1*2)+1/(2*3)+1/(3*4)+……+1/(99*100)】
=99-【(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/99-1/100)】
=99-【1/1-1/100】
=99-99/100
=9801/100