数学培优题,请详细分析每一步.(日期09.09)第1题:(11-11/36)+(9-11/36×5)+(1-11/36×3)+(5-11/36×9)+(3-11/36×7)+(7-11/36×11)第2题:1*1/8×1*1/9×1*1/10×1*1/11×1*1/12×1*1/13 注:*是“又”的意思第3题:4×5*3/4+5×6*4/5+6×7*5/6+7×8*6/7+8×9*7/8+8 注:*是“又”的意思第4题:1-1/3-1/9-1/27-1/81-1/243-1/729-1/2189
2019-06-02
数学培优题,请详细分析每一步.(日期09.09)
第1题:(11-11/36)+(9-11/36×5)+(1-11/36×3)+(5-11/36×9)+(3-11/36×7)+(7-11/36×11)
第2题:1*1/8×1*1/9×1*1/10×1*1/11×1*1/12×1*1/13 注:*是“又”的意思
第3题:4×5*3/4+5×6*4/5+6×7*5/6+7×8*6/7+8×9*7/8+8 注:*是“又”的意思
第4题:1-1/3-1/9-1/27-1/81-1/243-1/729-1/2189
优质解答
(11-11/36)+(9-11/36×5)+(1-11/36×3)+(5-11/36×9)+(3-11/36×7)+(7-11/36×11)
=(11+9+1+5+3+7)-(11/36)(1+5+3+9+7+11)
=(1-11/36)×(1+3+5+7+9+11)
=25/36×36
=25
1*1/8×1*1/9×1*1/10×1*1/11×1*1/12×1*1/13
=(9/8)×(10/9)×(11/10)×(12/11)×(13/12)×(14/13)
=(9×10×11×12×13×14)/(8×9×10×11×12×13)
=14/8
=7/4
4×5*3/4+5×6*4/5+6×7*5/6+7×8*6/7+8×9*7/8+8
=4×(6-1/4)+5×(7-1/5)+6×(8-1/6)+7×(9-6/7)+8×(10-1/8)+8
=4×6-1+5×7-1+6×8-1+7×9-1+8×10-1+8
=24+35+48+63+80+3
=253
1-1/3-1/9-1/27-1/81-1/243-1/729-1/2189
=1-(1/3+1/9+1/27+1/81+1/243+1/729+1/2189)
=1-(1/3)[1-(1/3)^7]/(1-1/3)
=1-(1094/2189)
=1095/2189
(11-11/36)+(9-11/36×5)+(1-11/36×3)+(5-11/36×9)+(3-11/36×7)+(7-11/36×11)
=(11+9+1+5+3+7)-(11/36)(1+5+3+9+7+11)
=(1-11/36)×(1+3+5+7+9+11)
=25/36×36
=25
1*1/8×1*1/9×1*1/10×1*1/11×1*1/12×1*1/13
=(9/8)×(10/9)×(11/10)×(12/11)×(13/12)×(14/13)
=(9×10×11×12×13×14)/(8×9×10×11×12×13)
=14/8
=7/4
4×5*3/4+5×6*4/5+6×7*5/6+7×8*6/7+8×9*7/8+8
=4×(6-1/4)+5×(7-1/5)+6×(8-1/6)+7×(9-6/7)+8×(10-1/8)+8
=4×6-1+5×7-1+6×8-1+7×9-1+8×10-1+8
=24+35+48+63+80+3
=253
1-1/3-1/9-1/27-1/81-1/243-1/729-1/2189
=1-(1/3+1/9+1/27+1/81+1/243+1/729+1/2189)
=1-(1/3)[1-(1/3)^7]/(1-1/3)
=1-(1094/2189)
=1095/2189