计算1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024
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计算1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024
![计算1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024](/uploads/image/z/802776-48-6.jpg?t=%E8%AE%A1%E7%AE%971%2F2%2B1%2F4%2B1%2F8%2B1%2F16%2B1%2F32%2B1%2F64%2B1%2F128%2B1%2F256%2B1%2F512%2B1%2F1024)
用裂项法解,1/2 = 1 - 1/2,1/4 = 1/2 - 1/4,1/8 = 1/4 - 1/8,原式就等于
1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 ...+ 1/512 - 1/1024
所以=1 - 1/1024 = 1023/1024
1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 ...+ 1/512 - 1/1024
所以=1 - 1/1024 = 1023/1024