1 + 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/1024
= (1/2 + 1/4 + 1/8 + 1/16 + ... + 1/1024) + 1
1/2 + 1/4 = 1 - 1/4
1/2 + 1/4 + 1/8 = 1 - 1/8
1/2 + 1/4 + 1/8 + 1/16 = 1 - 1/16
Vậy:
(1/2 + 1/4 + 1/8 + 1/16 + ... + 1/1024) + 1
= 1 - 1/1024 + 1
= 1023/1024 + 1
= 1 1023/1024