1/1x2x3x4+1/2x3x4x5+1/3x4x5x6+1/4x5x6x7+1/5x6x7x8+1/6x7x8x9+
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/23 20:24:44
1/1x2x3x4+1/2x3x4x5+1/3x4x5x6+1/4x5x6x7+1/5x6x7x8+1/6x7x8x9+1/7x8x9x10 求简算
1/(1×2×3×4)+1/(2×3×4×5)+1/(3×4×5×6)+...+1/(7×8×9×10)
=(1/3)×[1/(1×2×3)-1/(2×3×4)]+(1/3)×[1/(2×3×4)-1/(3×4×5)]+(1/3)×[1/(3×4×5)-1/(4×5×6)]+...+(1/3)×[1/(7×8×9)-1/(8×9×10)]
=(1/3)×[1/(1×2×3)-1/(2×3×4)+1/(2×3×4)-1/(3×4×5)+1/(3×4×5)-1/(4×5×6)+...+1/(7×8×9)-1/(8×9×10)]
=(1/3)×[1/(1×2×3)-1/(8×9×10)]
=(1/3)×[(1/6)-(1/720)]
=(1/3)×(119/720)
=119/2160
=(1/3)×[1/(1×2×3)-1/(2×3×4)]+(1/3)×[1/(2×3×4)-1/(3×4×5)]+(1/3)×[1/(3×4×5)-1/(4×5×6)]+...+(1/3)×[1/(7×8×9)-1/(8×9×10)]
=(1/3)×[1/(1×2×3)-1/(2×3×4)+1/(2×3×4)-1/(3×4×5)+1/(3×4×5)-1/(4×5×6)+...+1/(7×8×9)-1/(8×9×10)]
=(1/3)×[1/(1×2×3)-1/(8×9×10)]
=(1/3)×[(1/6)-(1/720)]
=(1/3)×(119/720)
=119/2160
观察下列各式:1x2x3x4+1=25=5^2,2x3x4x5+1=121=11^2,3x4x5x6+1=361=19^
这道题怎样巧算1/1x2x3x4+1/2x3x4x5+.+1/7x8x9x10
求规律 根号1x(乘法的意思)2x3x4+1=5 根号2x3x4x5+1=11 根号3x4x5x6+1=19 根号4x5
观察下列等式:1X2=1/3X1X2X3;1X2+2X3=1/3X2X3X4;1X2+2X3+3X4=1/3X3X4X5
1/1X2+2/1X2X3+3/1X2X3X4+4/1X2X
观察下列各式:第一式:1x2x3x4+1
1X2X3X4+1=_______=( )的平方
给出下列算式:1x2x3x4+1=25;2x3x4x5x6+1=121;3x4x5x6x7+1=361……
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