一题有理数的题目,1+（1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256）=?怎么算?
问题描述：
一题有理数的题目,1+（1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256）=?怎么算?
答
原式=1+（1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/256）-1/256
=1+（1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128）-1/256
=1+（1/2+1/4+1/8+1/16+1/32+1/64+1/64）-1/256
=1+（1/2+1/4+1/8+1/16+1/32+1/32）-1/256
=1+（1/2+1/4+1/8+1/16+1/16）-1/256
=1+（1/2+1/4+1/8+1/8）-1/256
=1+（1/2+1/4+1/4）-1/256
=1+（1/2+1/2）-1/256
=2-1/256
=1又255/256
答
511/256
过程：=1+(1-1/2+1/2-1/4+1/4-1/8+……+1/64-1/128+1/128-1/256)
=1+1-1/256
答
1+（1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256）=1+(1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32+1/32-1/64+1/64-1/128+1/128-1/256)=1+(1-1/256)=1+255/256=256/256+255/256=511/256