1/2+1/4+1/8+...+1/512+1/1024=

1/2+1/4+1/8+...+1/512+1/1024=
1/2+1/4+1/8+...+1/512+1/1024=

1/2+1/4+1/8+...+1/512+1/1024=
1/2+¼+...+1/256+1/512+1/1024
=1/2+¼+...+1/256+1/512+1/1024+(1/1024-1/1024)
=1/2+¼+...+1/256+1/512+1/512-1/1024
=1/2+¼+...+1/256+1/256-1/1024
=...
=1-1/1024
=1023/1024

1023/1024

运用等比数列的前n项和公式
结果为：1023/1024

此题为等比数列 求和 公比为1/2有等比数列求和公式的（1/2-1/1024*1/2）/（1-1/2）＝1023/1024