原式
= 1/(1*2) + 1/(2*3) + 1/(3*4) + ... + 1/(99*100)
= (1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + ... (1/99 - 1/100)
= 1 - 1/100
= 99/100
= 0.99