Question

一乘二分之一加二乘三分之一加三乘四分之一加……九十八乘九九分之一加九九乘一百

Answer 1

1/n(n+1)=1/n-1/(n+1)

1/(1*2)+1/(2*3)+1/(3*4)+…+1/(98*99)+1/(99*100)

=1-1/2+1/2-1/3+1/3-1/4+…+1/98-1/99+1/99-1/100

=1-1/100

=99/100