1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ... + 1/99 - 1/100
= (1 + 1/3 + 1/5 + ... + 1/99) - (1/2 + 1/4 + ... + 1/100)
= (1+1/3+1/5+...+1/99) - (1/2+1/4+...+1/100) + (1/2+1/4+...+1/100) - (1/2+1/4+...+1/100)
= [(1+1/3+1/5+...+1/99) + (1/2+1/4+...+1/100)] - [(1/2+1/4+...+1/100) - (1/2+1/4+...+1/100)]
= (1+1/2+1/3+1/4+...+1/100) - (1/2+1/4+...+1/100)×2
= (1+1/2+1/3+1/4+...+1/100) - (1/1+1/2+...+1/50)
= 1/51+1/52+..+1/100 (đpcm)
