UC知道用简便方法计算1024+512+256+128……+8+4+2+1+1/2+1/4+1/8……1/512+1/1024
来源：百度知道 编辑：UC知道 时间：2024/05/12 16:26:33
后面的分数是前面数的倒数，请写出计算步骤。谢谢大家！！小学六年级的。
1024+512+256+128……+8+4+2+1+1/2+1/4+1/8……1/512+1/1024
=1024+512+256+128……+8+4+2+1+1/2+1/4+1/8……1/512+1/1024+1/1024-1/1024
=1024+512+256+128……+8+4+2+1+1/2+1/4+1/8……1/512+1/512-1/1024
=1024+512+256+128……+8+4+2+1+1/2+1/4+1/8……1/256-1/1024
=1024+512+256+128……+8+4+2+1+1/2+1/4+1/8……1/126-1/024
=1024+512+256+128……+8+4+2+1+1/2+1/2-1/1024
=1024+512+256+128……+8+4+2+1+1-1/1024
=1024+512+256+128……+8+4+2+2-1/1024
=1024+512+256+128……+8+4+4-1/1024
=1024+512+512-1/1024
=1024+1024-1/1024
=2048-1/1024
=2047又1023/1024
S=1024+512+256+128……+8+4+2+1+1/2+1/4+1/8……1/512+1/1024
即：
S=2^10+2^9+2^8+....+2^1+2^0+2^-1+...+2^(-9)+2^(-10)
2S=2^11+2^10+2^9+..+2^2+2^1+2^0+.....+2^(-9)
相减：
S=2^11-2^(-10)
=2048-1/1024
=2047又1023/1024
当然了，学过数列后，你可以直接利用公式：
S=2^10*(1-1/2^21)/(1-1/2)
=2^11*(1-1/2^21)
=2^11-1/2^10
=2048-1/1024
=2047又1023/1024
a=1024+512+256+128……+8+4+2+1+1/2+1/4+1/8