1/2+1/4+1/8+1/16+.1/256+1/512
=1/2+1/4+1/8+1/16+.1/256+1/512+1/512-1/512
=1/2+1/4+1/8+1/16+.1/256+1/256-1/512
=1/2+1/4+1/8+1/16+.1/128-1/512
=...
=1/2+1/2-1/512
=1-1/512
=511/512
1/2+1/4+1/8+1/16+.1/256+1/512
=1/2+1/4+1/8+1/16+.1/256+1/512+1/512-1/512
=1/2+1/4+1/8+1/16+.1/256+1/256-1/512
=1/2+1/4+1/8+1/16+.1/128-1/512
=...
=1/2+1/2-1/512
=1-1/512
=511/512