1 × 2 / 1 + 2 × 3 / 1 + 3 × 4 / 1 + +1 / 99 × 101=

1 × 2 / 1 + 2 × 3 / 1 + 3 × 4 / 1 + 4 × 5 / 1 +. + 99 × 100 / 1
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+…… +1/99-1/100
=1-1/100
=99/100
=0.99