应该是(1-1/2)×(1-1/3)×(1-1/4)……×(1-1/100)吧?
(1-1/2)×(1-1/3)×(1-1/4)……×(1-1/100)
=(1/2)*(2/3)*(3/4)*.*(99/100)=1/100.
1/2+1/4+1/8+1/16+……+1/256
=1/2+1/4+1/8+1/16+……+1/256+1/256-1/256
=1/2+1/4+1/8+1/16+……+1/128-1/256
=.
=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.