问几道数学思考题⑴62又80/89×1/9⑵9又4/5＋99又4/5＋999又4/5＋9999又4/5＋4/5⑶2006÷2006又2006/2007⑷1×3＋2×6＋3×9＋4×12＋5×15/1×2＋2×4＋3×6＋4×8＋5×10⑸84又4/19×1.375＋105又5/19×0.9⑹(1＋1/2) ×(1－1/2

问几道数学思考题⑴62又80/89×1/9⑵9又4/5＋99又4/5＋999又4/5＋9999又4/5＋4/5⑶2006÷2006又2006/2007⑷1×3＋2×6＋3×9＋4×12＋5×15/1×2＋2×4＋3×6＋4×8＋5×10⑸84又4/19×1.375＋105又5/19×0.9⑹(1＋1/2) ×(1－1/2
问几道数学思考题
⑴62又80/89×1/9
⑵9又4/5＋99又4/5＋999又4/5＋9999又4/5＋4/5
⑶2006÷2006又2006/2007
⑷1×3＋2×6＋3×9＋4×12＋5×15/1×2＋2×4＋3×6＋4×8＋5×10
⑸84又4/19×1.375＋105又5/19×0.9
⑹(1＋1/2) ×(1－1/2) ×(1＋1/3) ×(1－1/3) ×…×(1＋1/100) ×(1－1/100)
⑺(1－1/2×1/2) ×(1－1/3×1/3) ×(1－1/4×1/4) ×…×(1－1/100×1/100)

问几道数学思考题⑴62又80/89×1/9⑵9又4/5＋99又4/5＋999又4/5＋9999又4/5＋4/5⑶2006÷2006又2006/2007⑷1×3＋2×6＋3×9＋4×12＋5×15/1×2＋2×4＋3×6＋4×8＋5×10⑸84又4/19×1.375＋105又5/19×0.9⑹(1＋1/2) ×(1－1/2
⑴62又80/89×1/9
=[63-9/89]*1/9
=63*1/9-9/89*1/9
=7-1/89
=6又80/89
⑵9又4/5＋99又4/5＋999又4/5＋9999又4/5＋4/5
=[9+99+999+9999]+4/5*5
=[10+100+1000+10000-4]+4
=11110
⑶2006÷2006又2006/2007
=2006/[2006（1+1/2007）]
=1/[2008/2007]
=2007/2008
⑷1×3＋2×6＋3×9＋4×
12＋5×15/1×2＋2×4＋3×6＋4×8＋5×10
=1*3[1+2*2+3*3+4*4+5*5]/[1*2（1+2*2+3*3+4*4+5*5]
=1*3/1*2
=3/2
⑸84又4/19×1.375＋105又5/19×0.9
=2200/19+1800/19
=4000/19
⑹(1＋1/2) ×(1－1/2) ×(1＋1/3) ×(1－1/3) ×…×(1＋1/100) ×(1－1/100)
=3/2*1/2*4/3*2/3*.*101/100*99/100
=1/2*101/100
=101/200
⑺(1－1/2×1/2) ×(1－1/3×1/3) ×(1－1/4×1/4) ×…×(1－1/100×1/100)
=[1-1/2][1+1/2][1-1/3][1+1/3].[1-1/10][1+1/10]
=1/2*3/2*2/3*4/3.9/10*11/10
=1/2*11/10
=11/20

⑴62又80/89×1/9
=(63-9/89)*1/9
=63*1/9-9/89*1/9
=7-1/89
=6又88/89
⑵9又4/5＋99又4/5＋999又4/5＋9999又4/5＋4/5
=(9又4/5+1/5)＋(99又4/5+1/5)＋(999又4/5+1/5)＋(9999又4/5+1/5)
=10+100+1000+1000...

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⑴62又80/89×1/9
=(63-9/89)*1/9
=63*1/9-9/89*1/9
=7-1/89
=6又88/89
⑵9又4/5＋99又4/5＋999又4/5＋9999又4/5＋4/5
=(9又4/5+1/5)＋(99又4/5+1/5)＋(999又4/5+1/5)＋(9999又4/5+1/5)
=10+100+1000+10000
=11110
⑶2006÷2006又2006/2007
=2006/[(2006*2007+2006)/2007]
=2006/[2006*2008/2007]
=2006*[2007/(2006*2008)]
=(2006*2007)/(2006*2008)
=2007/2008
⑷1×3＋2×6＋3×9＋4×12＋5×15/1×2＋2×4＋3×6＋4×8＋5×10
=[1*3+2*(1*3)+3*(1*3)+4*(1*3)+5*(1*3)]/[1*2+2*(1*2)+3*(1*2)+4*(1*2)+5*(1*2)]
=[(1*3)*(1+2+3=4+5)]/[(1*2)*(1+2+3+4+5)]
=3/2
⑸84又4/19×1.375＋105又5/19×0.9
=(21又1/19)*4*1.375＋(21又1/19)*5*0.9
=21又1/19*5.5+21又1/19*4.5
=21又1/19*(5.5+4.5)
=21又1/19*10
=21*10+1/19*10
=210+10/19
=210又10/19
⑹(1＋1/2) ×(1－1/2) ×(1＋1/3) ×(1－1/3) ×…×(1＋1/100) ×(1－1/100)
=1/2*1/2*4/3*2/3*......*101/100*99/100
=1/2*101/100
=101/200
⑺(1－1/2×1/2) ×(1－1/3×1/3) ×(1－1/4×1/4) ×…×(1－1/100×1/100)
=(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*(1+1/4)*(1-1/4)*......*(1+1/100)*(1-1/100)
=1/2*1/2*4/3*2/3*......*101/100*99/100
=1/2*101/100
=101/200

收起

⑴62又80/89×1/9=(63-1/89)×1/9 =7-1/801=6又800/801
⑵9又4/5＋99又4/5＋999又4/5＋9999又4/5＋4/5=(10-1/5)+(100-1/5)+(1000-1/5)+(10000-1/5)+(1-1/5)=11111-1=11110
⑶2007/2008
⑷1×3＋2×6＋3×9＋4×12＋5×15/1×2＋2×4＋3×6＋4×8＋5×10
=[(1×3)(1+4+9+16+25)]/[(1×2)(1+4+9+16+25)]=1.5