1/2+1/4+1/8+1/16+1/32+...+1/1024简便计算

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1/2+1/4+1/8+1/16+1/32+...+1/1024简便计算1/2+1/4+1/8+1/16+1/32+...+1/1024简便计算1/2+1/4+1/8+1/16+1/32+...+1/

1/2+1/4+1/8+1/16+1/32+...+1/1024简便计算
1/2+1/4+1/8+1/16+1/32+...+1/1024简便计算

1/2+1/4+1/8+1/16+1/32+...+1/1024简便计算
你好：

1/2+1/4+1/8+1/16+1/32+...+1/1024
=（1-1/2）+（1/2-1/4）+（1/4-1/8）+（1/8-1/16）…………+（1/152-1/1024）
=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16…………+1/152-1/1024
=1-1/1024
=1023/1024

1/2+1/4+1/8+1/16+1/32+...+1/1024
=1/2+1/4+1/8+..+1/1024+1/1024-1/1024
=1/2+1/4+1/8+..+1/512-1/1024
。。
=1-1/1024
=1023/1024

设A=1/2+1/4+1/8+1/16+1/32+...+1/1024 ①
2A=1+1/2+1/4+1/8+1/16+1/32+...+1/502 ②
②-① A=1-1/1024=1023/1024