Question

一道数学题，拜托，好心人帮下忙。

1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
需要过程和解释，谢谢了

Answer 1

这个是分母加倍的加法，规律如下
1/2=1-1/2
1/4=1/2-1/4
1/8=1/4-1/8
。。。。

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

Answer 2

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

Answer 3

设x=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
则2x=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128
2x-x=1-1/256
即x=255/256

Answer 4

原式=1／2+（1／2）^2+（1／2）^3+（1／2）^4+（1／2）^5+(1／2)^6+（1／2）^7+（1／2）^8
=1／2×((1-(1／2)^8))／(1-1／2)
=1-(1／2)^8
=255／256

Answer 5

原式=1/2*(1-1/2^8)/(1-1/2)=255/256
这是等比数列的求和问题。
s即式子的和，a为式子的首项，q为公比，即后一项除以后一项,n为项数。
s=a*（1-q^n)/(1-q)

Answer 6

128/256+64/256+32/256+8/256+4/256+2/256+1/256=239/256