用简便方法计算1⼀2+1⼀4+1⼀8+……+1⼀256。

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

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

基本的裂项啊,把1/2裂成1-1/2,把1/4裂成1/2-1/4,以此类推,第二个也是,你会发现都被消掉了,就可以算了,祝学业成功.

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)