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计算,1/2x4+1/4x6+1/6x8+......+1/48x50=?,1/2+1/6+1/12+1/20+1/30+1/42=
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答:两道题目考查的都是分数的裂项:
1/(2x4)+1/(4x6)+1/(6x8)+......+1/(48x50)
=(1/2)x(1/2-1/4+1/4-1/6+1/6-1/8+....+1/48-1/50)
=(1/2)x(1/2-1/50)
=1/4-1/100
=6/25
1/2+1/6+1/12+1/20+1/30+1/42
=1/(1x2)+1/(2x3)+1/(3x4)+......+1/(6x7)
=1-1/2+1/2-1/3+...+1/6-1/7
=1-1/7
=6/7
1/(2x4)+1/(4x6)+1/(6x8)+......+1/(48x50)
=(1/2)x(1/2-1/4+1/4-1/6+1/6-1/8+....+1/48-1/50)
=(1/2)x(1/2-1/50)
=1/4-1/100
=6/25
1/2+1/6+1/12+1/20+1/30+1/42
=1/(1x2)+1/(2x3)+1/(3x4)+......+1/(6x7)
=1-1/2+1/2-1/3+...+1/6-1/7
=1-1/7
=6/7
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等于(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+…+(1/48-1/50)=1/2-1/50=25/50-1/50
=24/50=12/25。
=24/50=12/25。
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1/2x4+1/4x6+1/6x8+…+1/48x50
=2/1+3/2+4/3+5/4+6/5+7/6+8/7+9/8+10/9+11/10+12/11+13/12+14/13+15/14+16/15+17/16+18/17+19/18+20/19+21/20+22/21+23/22+24/23+25/24
=27.77595818
1/2+1/6+1/12+1/20+1/30+1/42
=4/6+1/42+(3+2)/60+1/12
=2/3+1/42+1/12+1/12
=29/42+1/6
=29/42+7/42
=36/42
=6/7
=2/1+3/2+4/3+5/4+6/5+7/6+8/7+9/8+10/9+11/10+12/11+13/12+14/13+15/14+16/15+17/16+18/17+19/18+20/19+21/20+22/21+23/22+24/23+25/24
=27.77595818
1/2+1/6+1/12+1/20+1/30+1/42
=4/6+1/42+(3+2)/60+1/12
=2/3+1/42+1/12+1/12
=29/42+1/6
=29/42+7/42
=36/42
=6/7
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