数学题...进来解

由1/2+1/4=3/4,
1/2+1/4+1/8=7/8,
1/2+1/4+1/8+1/16=17/16.
所以1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=255/256

乘256就变成了2一次放加......加到2的8次方,用等比数列求和公式即可 再除256.....好象麻烦了点
哦,对了,另这个式子=t然后乘2 两式相减就知道怎么做了拉呵呵

原式=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+
1/256-1/256
=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128-1/256
=1/2+1/4+1/8+1/16+1/32+1/64+1/64-1/256
.
.
=1-1/256
=255/256

=256*（1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256）/256
=（128+64+32+16+8+4+2+1）/256
=255/256

1/256(128+64+32+16+8+4+2+1)=1/256<(128+32)+(64+16)+(8+2)+(4+1)>=255/256
晕这个不是很简便
记得有一种方法不太清楚了

1/2=1/2=(2^1-1)/2^1
1/2+1/4=3/4=(2^2-1)/2^2
1/2+1/4+1/8=7/8=(2^3-1)/2^3
1/2+1/4+1/8+1/16=15/16= (2^4-1)/2^4
......
1/2+1/4+1/8+1/16+......+1/2^n=(2^n-1)/2^n

所以
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=(256-1)/256
=255/256