3/2+5/4+9/8+17/16+.+513/512=?

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3/2+5/4+9/8+17/16+.+513/512=?3/2+5/4+9/8+17/16+.+513/512=?3/2+5/4+9/8+17/16+.+513/512=?3/2+5/4+9/8+1

3/2+5/4+9/8+17/16+.+513/512=?
3/2+5/4+9/8+17/16+.+513/512=?

3/2+5/4+9/8+17/16+.+513/512=?
3/2+5/4+9/8+17/16+.+513/512
=1+1/2+1+1/4+1+1/8+1+1/16+.+1+1/512
=9+(1/2+1/4+1/8+1/6+.+1/512)
=9+(1/2+1/4+1/8+1/6+.+1/256+1/512+1/512)-1/512
=9+(1/2+1/4+1/8+1/6+.+1/256+1/256)-1/512
=.
=9+1-1/512
=10-1/512
=9又511/512

9+512分之511

9又511/512

原式=1+1/2+1+1/4+1+1/8+......+1+1/512=9+1/2+1/(2^2)+1/(2^3)+......+1/(2^9)=9+512/513
后面那部分用等比数列算

3/2+5/4+9/8+17/16+。。。。。。+513/512
=1+1/2+1+1/4+1+1/8+1+1/16+-------+1+1/512
=1+1+1+-----+1(共9个1)+1/2+1/4+1/8+1/16+------+1/512 512是2的9次方
=9+1/2(1-1/2的9次方)/(1-1/2)
=9+511/512
=9又511/512
望采纳!!!