Ta có: A = 5/2 + 5/6 + 5/12 + 5/20 + 5/30 + .... + 5/9900
= 5/1.2 + 5/2.3 + 5/3.4 + 5/4.5 + 5/5.6 + .... + 5/99.100
= 5. (1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + .... + 1/99.100)
= 5. (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + ...+ 1/99 - 1/100)
= 5 . (1 - 1/100)
= 5. 99/100 = 99/20
