1/2+1/4+1/8+1/16+.+1/512结果是多少

来源：学生作业帮助网编辑：作业帮时间：2024/05/05 01:40:22

1/2+1/4+1/8+1/16+.+1/512结果是多少
1/2+1/4+1/8+1/16+.+1/512结果是多少

1/2+1/4+1/8+1/16+.+1/512结果是多少
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