计算 1⼀2+3⼀4+7⼀8+15⼀16+31⼀32+63⼀64+127⼀128+255⼀256

1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/256
=（1-1/2)+(1-1/4)+(1-1/8)+(1-1/16)+(1-1/32)+(1-1/64)+(1-1/128)+(1-1/256)
=1*8-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256)
=8-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/256)+1/256
=8-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128)+1/256
=8-(1/2+1/4+1/8+1/16+1/32+1/64+1/64)+1/256
=8-(1/2+1/4+1/8+1/16+1/32+1/32)+1/256
=8-(1/2+1/4+1/8+1/16+1/16)+1/256
=8-(1/2+1/4+1/8+1/8)+1/256
=8-(1/2+1/4+1/4)+1/256
=8-(1/2+1/2)+1/256
=8-1+1/256
=7+1/256
所以，结果为：
七又二百五十六分之一
欢迎采纳，
轻松一下！
O(∩_∩)O哈！

1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/256
=(1-1/2)+(1-1/4)+(1-1/8)+...+(1-1/256)
=8-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256)
括号里面就是个等比数列，可以用公式求和
如果没学过等比数列，可以用下面的方法：
设m=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
都乘2，得：
2m=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128
相减，得：
m=1-1/256=255/256
原式=8-m
=8-255/256
=7又1/256

1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/256
=1-1/2+1-1/4+1-1/8+1-1/16+1-1/32+1-1/64+1-1/128+1-1/256
=8-(1/2+1/4+....+1/256)
=8-{1/2[1-(1/2)^8]/(1-1/2)}
=8-1/256
=2047/256

1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/256
=(1-1/2)+(1-1/4)+(1-1/8)+...+(1-1/256)
=8-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256)
括号里面就是个等比数列，可以用公式求和
6年级，没学过等比数列，可以用下面的方法：
设m=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
都乘2，得：
2m=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128
相减，得：
m=1-1/256=255/256
原式=8-m
=8-255/256
=7又1/256

原式=(1/2+1/2)+(3/4+1/4)+(7/8+1/8)+.....(255/256+1/256) -(1/2+1/4+1/8+....1/256)
=8-(1/2+1/4+1/8+...+1/128+1/256+1/256)-1/256
=8-(1/2+1/4+....+1/128+1/128)+1/256
....
=8-1+1/256
=7+1/256