Question

1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256=？（越快越好，谢谢了）

Answer 1

1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
a1=1/2 q=1/2
S8=a1*(1-q^n)/(1-q) =1/2 * [1-（1/2)^8]/(1-1/2)=255/256

Answer 2

等比数列和公式(1/2-((1/256)*(1/2))/(1-1/2)=（256/512-1/512）/(1/2)=255/256

Answer 3

255/256
再加上1/512就是511/512

Answer 4

换算为2的N次幂分之一

Answer 5

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
=1/2+1/4+1/8+1/8-1/256
=1/2+1/4+1/4-1/256
=1/2+1/2-1/256
=1-1/256
=255/256