观察下列各式:1乘2=1/3(1乘2乘3-0乘1乘2),2乘3=1/3(2乘3乘4-1乘2乘3),3乘4=1/3×(3×4×5-2×3×4)读完以上材料,请你计算下列各题1×2+2×3+3×4+.+10×11(写出过程)1×2+2×3+3×4+.+n×(n+1)=1×2×3+2×3×4+3×4×5+.7×8
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/22 17:20:58
![观察下列各式:1乘2=1/3(1乘2乘3-0乘1乘2),2乘3=1/3(2乘3乘4-1乘2乘3),3乘4=1/3×(3×4×5-2×3×4)读完以上材料,请你计算下列各题1×2+2×3+3×4+.+10×11(写出过程)1×2+2×3+3×4+.+n×(n+1)=1×2×3+2×3×4+3×4×5+.7×8](/uploads/image/z/3768968-56-8.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%3A1%E4%B9%982%3D1%2F3%281%E4%B9%982%E4%B9%983-0%E4%B9%981%E4%B9%982%29%2C2%E4%B9%983%3D1%2F3%282%E4%B9%983%E4%B9%984-1%E4%B9%982%E4%B9%983%29%2C3%E4%B9%984%3D1%2F3%C3%97%EF%BC%883%C3%974%C3%975-2%C3%973%C3%974%29%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%E4%B8%8B%E5%88%97%E5%90%84%E9%A2%981%C3%972%2B2%C3%973%2B3%C3%974%2B.%2B10%C3%9711%EF%BC%88%E5%86%99%E5%87%BA%E8%BF%87%E7%A8%8B%EF%BC%891%C3%972%2B2%C3%973%2B3%C3%974%2B.%2Bn%C3%97%28n%2B1%29%3D1%C3%972%C3%973%2B2%C3%973%C3%974%2B3%C3%974%C3%975%2B.7%C3%978)
观察下列各式:1乘2=1/3(1乘2乘3-0乘1乘2),2乘3=1/3(2乘3乘4-1乘2乘3),3乘4=1/3×(3×4×5-2×3×4)读完以上材料,请你计算下列各题1×2+2×3+3×4+.+10×11(写出过程)1×2+2×3+3×4+.+n×(n+1)=1×2×3+2×3×4+3×4×5+.7×8
观察下列各式:1乘2=1/3(1乘2乘3-0乘1乘2),2乘3=1/3(2乘3乘4-1乘2乘3),3乘4=1/3×(3×4×5-2×3×4)
读完以上材料,请你计算下列各题
1×2+2×3+3×4+.+10×11(写出过程)
1×2+2×3+3×4+.+n×(n+1)=
1×2×3+2×3×4+3×4×5+.7×8×9=
观察下列各式:1乘2=1/3(1乘2乘3-0乘1乘2),2乘3=1/3(2乘3乘4-1乘2乘3),3乘4=1/3×(3×4×5-2×3×4)读完以上材料,请你计算下列各题1×2+2×3+3×4+.+10×11(写出过程)1×2+2×3+3×4+.+n×(n+1)=1×2×3+2×3×4+3×4×5+.7×8
一、
1*2+2*3+3*4+……+10*11
=1/3【(1*2*3-0*1*2)+(2*3*4-1*2*3)+……+(10*11*12-9*10*11)】
=1/3(1*2*3-0*1*2+2*3*4-1*2*3+……+10*11*12-9*10*11)
=1/3(10*11*12-0*1*2)————每前一组的前一项的后一组的后一项抵消
=1/3(1320-0)
=1/3(1320)
=440
二、
原式= =1/3{【1*2*3-0*1*2】+【2*3*4-1*2*3】+……+【n*(n+1)*(n+2)-(n-1)*n*(n+1)】}
=1/3【n*(n+1)*(n+2)-0*1*2】
=1/3【n*n*n+3*n*n+2*n-0】
=1/3【n*n*n+3*n*n+2*n】
————暂时我无力化解
三、
总结以上规律
原式=1/4*1*2*3*4+1/4*[2*3*4*5-1*2*3*4]+...+1/4*[7*8*9*10-6*7*8*9]
=1/4[1*2*3*4+2*3*4*5-1*2*3*4+...+7*8*9*10-6*7*8*9]
=1/4*7*8*9*10
=1260