1x2x3+2x3x4+3x4x5+.+10x11x12
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/01 23:59:18
1x2x3+2x3x4+3x4x5+.+10x11x12
设第n项为an
an=n(n+1)(n+2)=n^3+3n^2+2n
1×2×3+2×3×4+...+10×11×12
=(1^3+2^3+...+10^3)+3(1^2+2^2+...+10^2)+2(1+2+...+10)
=[10(10+1)/2]^2+3×10×(10+1)(20+1)/6+2×10×11/2
=3025+1155+110
=4290
用到的公式:
1^3+2^3+...+n^3=[n(n+1)/2]^2
1^2+2^2+...+n^2=n(n+1)(2n+1)/6
1+2+3+...+n=n(n+1)/2
an=n(n+1)(n+2)=n^3+3n^2+2n
1×2×3+2×3×4+...+10×11×12
=(1^3+2^3+...+10^3)+3(1^2+2^2+...+10^2)+2(1+2+...+10)
=[10(10+1)/2]^2+3×10×(10+1)(20+1)/6+2×10×11/2
=3025+1155+110
=4290
用到的公式:
1^3+2^3+...+n^3=[n(n+1)/2]^2
1^2+2^2+...+n^2=n(n+1)(2n+1)/6
1+2+3+...+n=n(n+1)/2
1x2x3+2x3x4+3x4x5+.+10x11x12
1x2x3+2x3x4+3x4x5……+10x11x12巧算 请在两天之内回答
(1/2x3x4)+(1/3x4x5)+.+(1/10x11x12)
1/1x2x3+1/2x3x4+1/3x4x5
1x2X3+2x3X4+3x4X5+…+7X8X9=?
1x2x3+2x3x4+3x4x5+…+8x9x10
1x2x3+2x3x4+3x4x5+...+7x8x9=,
1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+.+1/48x49x50=
1/1x2x3+1/2x3x4+1/3x4x5+.+1/11x12x13=
1/1x2x3+1/2x3x4+1/3x4x5+.+1/9x10x11=
请1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6=
1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+.1/(20x21x22)=?