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:2024/11/18 05:26:58
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