1/2+1/4+1/8+...+1/256+1+512+1/1024的值上面的打错了，应是1/2+1/4+1/8+...+1/256+1/512+1/1024的值

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1/2+1/4+1/8+...+1/256+1+512+1/1024的值上面的打错了，应是1/2+1/4+1/8+...+1/256+1/512+1/1024的值
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1/2+1/4+1/8+...+1/256+1+512+1/1024的值上面的打错了，应是1/2+1/4+1/8+...+1/256+1/512+1/1024的值
1/2+1/4+1/8+...+1/256+1+512+1/1024的值
上面的打错了，应是1/2+1/4+1/8+...+1/256+1/512+1/1024的值

1/2+1/4+1/8+...+1/256+1+512+1/1024的值上面的打错了，应是1/2+1/4+1/8+...+1/256+1/512+1/1024的值
=1-1/2+1/2-1/4+1/4-1/8+...+1/128-1/256+1/256-1/512+1/512-1/1024
=1-1/1024
=1023/1024

1023/1024

S=1/2+1/4+1/8+...+1/256+1/512+1/1024
2S=1+1/2+1/4+1/8+...+1/256+1/512
相减
S=1-1/1024=1023/1024