Question

1/2+5/6+11/12+19/20+.9890/9900=

Answer 1

=(1-1/2)+(1-1/6)+(1-1/12)+(1-1/20)+....../9(1-1/9900)=1*99-1/(1*2)-1/(2*3)-1/(3*4)-1/(4*5)-......1/(98*99)-1/(99*100)=99-(1-1/2)-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-......(1/98-1/99)-(1/99-1/100)=99-1+1/100=98.01