5分之1+10分之1+20分之1+40分之1+.+1280分之1+1280分之1等于多少?

1/5 +1/10 +1/20 +1/40+...+1/1280 +1/1280
=(1/5)(1+1/2+1/4+1/8+...+1/256) +1/1280
=(1/5)(1/2^0 +1/2^1 +1/2^2+1/2^3+...+1/2^8) +1/1280
=(1/5)×(1-1/2^8)/(1-1/2) +1/1280
=(2/5)×255/256 +1/1280
=51/128+1/1280
=511/1280