Đặt S =(1-1/2)+(1-1/4)+(1-1/8)+...+(1-1/1024)
Ta có S=1/2+3/4+7/8+...+1023/1024
=1/2+3/2^2+7/2^3+...+1023/2^10
=> 2S=1+3/2+7/2^2+...+1023/2^9
=> 2S-S=S=(1+3/2+7/2^2+...+1023/2^9)-(1/2+3/2^2+7/2^3+...+1023/2^10)
=> S=1+(3/2-1/2)+7/2^2-3/2^2)+...+(1023/2^9-511/2^9)-1023/2^10
=(1+1+...+1) -1023/1024
9 số hạng 1
= 9-1023/1024
= 8193/1024.