先找规律然后再按规律计算:1/2+1/4=3/4 1/2+1/4+1/8=7/81/2+1/4+1/8+1/16=15/161/2+1/4+1/8+1/16+1/32=31/321/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 08:05:19
![先找规律然后再按规律计算:1/2+1/4=3/4 1/2+1/4+1/8=7/81/2+1/4+1/8+1/16=15/161/2+1/4+1/8+1/16+1/32=31/321/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256=?](/uploads/image/z/2722580-44-0.jpg?t=%E5%85%88%E6%89%BE%E8%A7%84%E5%BE%8B%E7%84%B6%E5%90%8E%E5%86%8D%E6%8C%89%E8%A7%84%E5%BE%8B%E8%AE%A1%E7%AE%97%EF%BC%9A1%2F2%2B1%2F4%3D3%2F4++++++1%2F2%2B1%2F4%2B1%2F8%3D7%2F81%2F2%2B1%2F4%2B1%2F8%2B1%2F16%3D15%2F161%2F2%2B1%2F4%2B1%2F8%2B1%2F16%2B1%2F32%3D31%2F321%2F2%2B1%2F4%2B1%2F8%2B1%2F16%2B1%2F32%2B1%2F64%2B1%2F128%2B1%2F256%3D%3F)
先找规律然后再按规律计算:1/2+1/4=3/4 1/2+1/4+1/8=7/81/2+1/4+1/8+1/16=15/161/2+1/4+1/8+1/16+1/32=31/321/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256=?
先找规律然后再按规律计算:
1/2+1/4=3/4
1/2+1/4+1/8=7/8
1/2+1/4+1/8+1/16=15/16
1/2+1/4+1/8+1/16+1/32=31/32
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256=?
先找规律然后再按规律计算:1/2+1/4=3/4 1/2+1/4+1/8=7/81/2+1/4+1/8+1/16=15/161/2+1/4+1/8+1/16+1/32=31/321/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256=?
是找规律的题
1/2+1/4=3/4=(2的2次方-1)/(2的2次方)
1/2+1/4+1/8=7/8=(2的3次方-1)/(2的3次方)
1/2+1/4+1/8+1/16=15/16=(2的4次方-1)/(2的4次方)
1/2+1/4+1/8+1/16+1/32=31/32=(2的5次方-1)/(2的5次方)
依次类推
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256=(2的7次方-1)/(2的7次方)
=255/256
也可不这样麻烦,看最后一个加数与和的规律:分母相同,分子减一;知结果为255/256
1/2+1/4=3/4=1-1/4
1/2+1/4+1/8=7/8=1-1/8
1/2+1/4+1/8+1/16=15/16=1-1/16
1/2+1/4+1/8+1/16+1/32=31/32=1-1/32
所以
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=1-1/256
=255/256
答案为:255/256
规律为:1/2+1/4+1/8+1/16+1/32+1/64+...+1/N=(N-1)/N