用简便方法计算1/2+1/4+1/8+……+1/256。

1/2=1-1/2
1/4=1/2-1/4
1/8=1/4-1/8
......
1/256=1/128-1/256
_____________________
1/2+1/4+1/8+…+1/256=1-1/256= 255/256

1/2+1/4+1/8+……+1/256
=(1-1/2)+(1/2-1/4)+(1/4-1/8)+......+(1/128-1/256)
=1-1/2+1/2-1/4+1/4-1/8+......+1/128-1/256
=1-1/256
=255/256

等比数列求和啊~~~
1/2+1/2^2...+1/2^8

3）求和公式：Sn=nA1(q=1)
Sn=A1(1-q^n)/(1-q)
=(a1-a1q^n)/(1-q)
=a1/(1-q)-a1/(1-q)*q^n ( 即A-Aq^n)
(前提：q不等于 1)

1/2+1/4+1/8+……+1/256＋1/256-1/256
=1/2+1/4+1/8+……+1/128+1/128-1/256
=1/2+1/4＋……＋1/64+1/64-1/256
=……
＝1－1/256

（1/2+1/4+1/8+……+1/256）
=（1/2+1/4+1/8+……+1/128+1/256）+1/256-1/256
=1/2+1/4+1/8+……+1/128+1/256+1/256-1/256
=1/2+1/4+1/8+……+1/128+1/128-1/256
=1/2+1/4+1/8+……+1/64+1/64-1/256
…………
=1/2+1/4+1/4-1/256
=1-1/256
=255/256

这形成了一个等比级数，比值为1/2，用等比级数公式来算。