1×2×3分之1+2×3×4分之1+3×4×5分之1+.+13×14×15分之1 简便计算简便计算 (1)1×2×3分之1+2×3×4分之1+3×4×5分之1+.+13×14×15分之1(2)8×9×10分之1+9×10×11分之1+10×11×12分之1+11×12×13分之1+12×13×14分
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/14 10:57:52
![1×2×3分之1+2×3×4分之1+3×4×5分之1+.+13×14×15分之1 简便计算简便计算 (1)1×2×3分之1+2×3×4分之1+3×4×5分之1+.+13×14×15分之1(2)8×9×10分之1+9×10×11分之1+10×11×12分之1+11×12×13分之1+12×13×14分](/uploads/image/z/34884-36-4.jpg?t=1%C3%972%C3%973%E5%88%86%E4%B9%8B1%2B2%C3%973%C3%974%E5%88%86%E4%B9%8B1%2B3%C3%974%C3%975%E5%88%86%E4%B9%8B1%2B.%2B13%C3%9714%C3%9715%E5%88%86%E4%B9%8B1+%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97+%EF%BC%881%EF%BC%891%C3%972%C3%973%E5%88%86%E4%B9%8B1%2B2%C3%973%C3%974%E5%88%86%E4%B9%8B1%2B3%C3%974%C3%975%E5%88%86%E4%B9%8B1%2B.%2B13%C3%9714%C3%9715%E5%88%86%E4%B9%8B1%EF%BC%882%EF%BC%898%C3%979%C3%9710%E5%88%86%E4%B9%8B1%2B9%C3%9710%C3%9711%E5%88%86%E4%B9%8B1%2B10%C3%9711%C3%9712%E5%88%86%E4%B9%8B1%2B11%C3%9712%C3%9713%E5%88%86%E4%B9%8B1%2B12%C3%9713%C3%9714%E5%88%86)
1×2×3分之1+2×3×4分之1+3×4×5分之1+.+13×14×15分之1 简便计算简便计算 (1)1×2×3分之1+2×3×4分之1+3×4×5分之1+.+13×14×15分之1(2)8×9×10分之1+9×10×11分之1+10×11×12分之1+11×12×13分之1+12×13×14分
1×2×3分之1+2×3×4分之1+3×4×5分之1+.+13×14×15分之1 简便计算
简便计算 (1)1×2×3分之1+2×3×4分之1+3×4×5分之1+.+13×14×15分之1
(2)8×9×10分之1+9×10×11分之1+10×11×12分之1+11×12×13分之1+12×13×14分之1
(3)1×2×3×4分之1+2×3×4×5分之1+3×4×5×6分之1+.+10×11×12×13分之1
(4)4分之1+28分之1+70分之1+130分之1+208分之1
1×2×3分之1+2×3×4分之1+3×4×5分之1+.+13×14×15分之1 简便计算简便计算 (1)1×2×3分之1+2×3×4分之1+3×4×5分之1+.+13×14×15分之1(2)8×9×10分之1+9×10×11分之1+10×11×12分之1+11×12×13分之1+12×13×14分
(4)原式=1/3(1-1/4)+1/3(1/4-1/7)+1/3(1/7-1/10)+1/3(1/10-1/13)+1/3(1/13-1/16)
=1/3(1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16)
=1/3(1-1/16)
=1/3*15/16
=5/16
【1-2分之一-3分之一】+【2分之一-3分之一-4分之一】+……一共等于【1-15分之一】等于15分之14
(1)原式= (1/2)[ (3-1)/(1X2X3) + (4-2)/(2X3X4) + (5-3)/(3X4X5) +……+ (15-13)/(13X14X15) ]
= (1/2)[ 1/(1X2) - 1/(2X3) + 1/(2X3) - 1/(3X4) + 1/(3X4) - 1/(4X5) +……+ 1/(13X14) - 1/(14X15) ]
= (1/...
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(1)原式= (1/2)[ (3-1)/(1X2X3) + (4-2)/(2X3X4) + (5-3)/(3X4X5) +……+ (15-13)/(13X14X15) ]
= (1/2)[ 1/(1X2) - 1/(2X3) + 1/(2X3) - 1/(3X4) + 1/(3X4) - 1/(4X5) +……+ 1/(13X14) - 1/(14X15) ]
= (1/2)[ 1/2 - 1/(14X15) ]
= (1/2)(105/210 - 1/210 )
= 26/105
(2)原式= (1/2)[ (10-8)/(8X9X10) + (11-9)/(9X10X11) +……+ (14-12)/(12X13X14) ]
= (1/2)[ 1/(8X9) - 1/(13X14) ]
= (1/2)( 1/72 - 1/182 )
=55/13104
(3)原式= (1/3)[ (4-1)/(1X2X3X4) + (5-2)/(2X3X4X5) + (6-3)/(3X4X5X6) +……+ (13-10)/(10X11X12X13) ]
= (1/3)[ 1/(1X2X3) - 1/(11X12X13) ]
= (1/3)( 1/6 - 1/1716 )
=95/1716
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