One half plus five sixths plus eleven twelfth plus nineteen twenties plus twenty-nine thirties. To 9899 9900 It's the method, not the calculation

One half plus five sixths plus eleven twelfth plus nineteen twenties plus twenty-nine thirties. To 9899 9900 It's the method, not the calculation

Using split term elimination method
=1-1/(1*2)+1-1/(2*3)+1-1/(3*4)+...+1-1/(99*100)
=99-(1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100)
=99-(1-1/100)=9801/100