A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024
2A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/246 + 1/512 + 1/1024
A = 1 - 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + 1/16 - 1/32 + 1/64 - 1/128 + 1/128 - 1/256 + 1/256 - 1/512 + 1/512 - 1/1024
A = 1 - 1/1024
A = 1023/1024
a = 1/2+1/4+1/8+1/16
= (1 - 1/2) + (1/2 -1/4) + (1/4 - 1/8) + ... + (1/512 - 1/1024).
= 1 - 1/1024
= 1023/1024
ta có : 1/2 + 1 /4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024
= 1-(1-1/2+1/2-1/8+1/8-1/16+1/16-1/32+1/32 -1/64+1/64-1/128+1/128 + 1/256+1/256 +1/512+1/512-1/1024
= 1 - 1/1024 = 1024/1024 - 1/1024 = 1/1024