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?
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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?
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?
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
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
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+1/3...
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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
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