1×2=1/3 (1×2×3-0×1×2) 2×3=1/3 (2×3×4-1×2×3) 3×4=1/3 (3×4×5-2×3×4) 由以上三个等式相加,可得1×2+2×3+3×4=(1/3)×3×4×5=20 读完以上材料,请你计算(1)1×2+2×3+3×4+…+n×(n+1)=_____ (2)1×2+2×3+3×4+…+10×11=_____
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 18:58:29
![1×2=1/3 (1×2×3-0×1×2) 2×3=1/3 (2×3×4-1×2×3) 3×4=1/3 (3×4×5-2×3×4) 由以上三个等式相加,可得1×2+2×3+3×4=(1/3)×3×4×5=20 读完以上材料,请你计算(1)1×2+2×3+3×4+…+n×(n+1)=_____ (2)1×2+2×3+3×4+…+10×11=_____](/uploads/image/z/11597739-51-9.jpg?t=1%C3%972%3D1%2F3+%281%C3%972%C3%973-0%C3%971%C3%972%29+2%C3%973%3D1%2F3+%282%C3%973%C3%974-1%C3%972%C3%973%29+3%C3%974%3D1%2F3+%283%C3%974%C3%975-2%C3%973%C3%974%29+%E7%94%B1%E4%BB%A5%E4%B8%8A%E4%B8%89%E4%B8%AA%E7%AD%89%E5%BC%8F%E7%9B%B8%E5%8A%A0%2C%E5%8F%AF%E5%BE%971%C3%972%2B2%C3%973%2B3%C3%974%3D%281%2F3%29%C3%973%C3%974%C3%975%3D20+%E8%AF%BB%E5%AE%8C%E4%BB%A5%E4%B8%8A%E6%9D%90%E6%96%99%2C%E8%AF%B7%E4%BD%A0%E8%AE%A1%E7%AE%97%281%291%C3%972%2B2%C3%973%2B3%C3%974%2B%E2%80%A6%2Bn%C3%97%28n%2B1%29%3D_____+%282%291%C3%972%2B2%C3%973%2B3%C3%974%2B%E2%80%A6%2B10%C3%9711%3D_____)
1×2=1/3 (1×2×3-0×1×2) 2×3=1/3 (2×3×4-1×2×3) 3×4=1/3 (3×4×5-2×3×4) 由以上三个等式相加,可得1×2+2×3+3×4=(1/3)×3×4×5=20 读完以上材料,请你计算(1)1×2+2×3+3×4+…+n×(n+1)=_____ (2)1×2+2×3+3×4+…+10×11=_____
1×2=1/3 (1×2×3-0×1×2) 2×3=1/3 (2×3×4-1×2×3) 3×4=1/3 (3×4×5-2×3×4) 由以上三个等式相加,可得1×2+2×3+3×4=(1/3)×3×4×5=20 读完以上材料,请你计算(1)1×2+2×3+3×4+…+n×(n+1)=_____ (2)1×2+2×3+3×4+…+10×11=_____(写出过程) (3)1×2×3+2×3×4+3×4×5+…+7×8×9=______
1×2=1/3 (1×2×3-0×1×2) 2×3=1/3 (2×3×4-1×2×3) 3×4=1/3 (3×4×5-2×3×4) 由以上三个等式相加,可得1×2+2×3+3×4=(1/3)×3×4×5=20 读完以上材料,请你计算(1)1×2+2×3+3×4+…+n×(n+1)=_____ (2)1×2+2×3+3×4+…+10×11=_____
(1)1×2+2×3+3×4+…+n×(n+1)= (1/3)n(n+1)(n+2)
(2)1×2+2×3+3×4+…+10×11= 1/3 (12×3-0×1×2) +1/3 (2×3×4-1×2×3)+…………+1/3(10x11x12-9x8x7)=1/3(10x11x12-0x1x2)=440
(3) .1260
(1)(1/3)*(n+1)*(n+2)
(2)(1/3)*10*11*12=440
(3)规律(1/4)*n*(n+1)*(n+2)*(n+3) 因此答案为(1/4)*7*8*9*10=1260
(1)1×2+2×3+3×4+…+n×(n+1)=_(n+1)(n+2)/3____ (2)1×2+2×3+3×4+…+10×11=(11+1)11_/3=44____(写出过程) (3)1×2×3+2×3×4+3×4×5+…+7×8×9=__180____