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](/uploads/image/z/134082-18-2.jpg?t=1%2F2%2B1%2F4%2B1%2F8%2B1%2F16%2B1%2F32%2B...%2B1%2F1024%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97)
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