作业帮1/2+1/4+1/8+1/16+……1/128=?要简便算法
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1/2+1/4+1/8+1/16+……1/128=?要简便算法
1/2+1/4+1/8+1/16+……1/128=?
要简便算法
1/2+1/4+1/8+1/16+……1/128=?要简便算法
必须根据小学的理解力来解题,高等方法不被接受
1/2+1/4+1/8+1/16+1/32+1/64+1/128
=(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128)-1/128
=(1/2+1/4+1/8+1/16+1/32+1/64+1/64)-1/128
=(1/2+1/4+1/8+1/16+1/32+1/32)-1/128
=(1/2+1/4+1/8+1/16+1/16)-1/128
=(1/2+1/4+1/8+1/8)-1/128
=(1/2+1/4+1/4)-1/128
=(1/2+1/2)-1/128
=1-1/128
=127/128
高中时候的等比数列，后边每一项都是前一项乘以1/2得到的。有公式的，前n项和Sn=a1（1-q的n次幂）/（1-q），最后为127/128
＝1－1／128＝127／128
1/2+1/4+1/8+1/16+1/32+1/64+1/128
=(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128)-1/128
=(1/2+1/4+1/8+1/16+1/32+1/64+1/64)-1/128
=(1/2+1/4+1/8+1/16+1/32+1/32)-1/128
=(1/2+1/4+1/8+1/16+1/16)-1/128
=(1/2+1/4+1/8+1/8)-1/128
=(1/2+1/4+1/4)-1/128
=(1/2+1/2)-1/128
=1-1/128
=127/128
分子为64+32+16+8+4+2+1=127，即一百二十八分之一百二十七！
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