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?

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