1/2+1/4+1/8+.+1/4096=(1-1/2)+(1/2-1/4)+(1/4-1/8)+(1/8-1/16)+.+(1/2048-1/4096)
=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+.+1/1024-1/2048+1/2048-1/4096
=1-1/4096
=4095/4096
1/2+1/4+1/8+.+1/4096=(1-1/2)+(1/2-1/4)+(1/4-1/8)+(1/8-1/16)+.+(1/2048-1/4096)
=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+.+1/1024-1/2048+1/2048-1/4096
=1-1/4096
=4095/4096