1x2x3+2x3x4+.+n(n+1)(n+2)=?
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1x2x3+2x3x4+.+n(n+1)(n+2)=?1x2x3+2x3x4+.+n(n+1)(n+2)=?1x2x3+2x3x4+.+n(n+1)(n+2)=?1/2(1/1*2-1/2*3)1/2
1x2x3+2x3x4+.+n(n+1)(n+2)=?
1x2x3+2x3x4+.+n(n+1)(n+2)=?
1x2x3+2x3x4+.+n(n+1)(n+2)=?
1/2(1/1*2-1/2*3) 1/2(1/2*3-1/3*4)...1/2［1/n*(n 1)-1/(n 1)*(n 2)］ =1/2*[1/1*2-1/(n 1)(n 2)]=1/4-1/2(n 1)(n 2) 1/(n*(n 1)*(n 2))=1/2*(1/(n*(n 1))-1/((n 1)*(n 2))) 所以:原式=1/2*((1/(1*2)-1/(2*3)) (1/(2*3)-1/(3*4)) ...) =1/2*(1/(1*2)-1/((n 1)*(n 2))) =1/4-1/(2*(n 1)*(n 2)) 就是将通项给分裂成两项比较容易处理的试一试就出来了 1/(1×2×3)=1/2×[1/(1×2)-1/(2×3)] 1/(2×3×4)=1/2×[1/(2×3)-1/(3×4)] 1/(3×4×5)=1/2×[1/(3×4)-1/(4×5)] .1/((n-1)n(n 2))=1/2×[1/((n-1)×n)-1/(n×(n 1))] 1/(n(n 1)(n 2))=1/2×[1/(n×(n 1))-1/((n 1)×(n 2))] 全部相加 =1/2×[1/(1×2)-1/((n 1)×(n 2)) ]
1X2X3+2X3X4+.+n(n+1)(n+2)
1x2x3+2x3x4+.+n(n+1)(n+2)=?
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1x2=(1/3)(1x2x3-0x1x2) 3x4=(1/3)(3x4x5-2x3x4) 问1x2x3+2x3x4+.+n(n+1)(n+2)=___________
1x2x3+2x3x4+...+nxx=?
1x2+2x3+3x4+...+n(n+1)=?1x2x3+2x3x4+3x4x5+...+n(n+1)(n+2)=?
1x2+2x3+3x4+...+nx(n+1)= 1x2x3＋2x3x4＋...＋n(n＋1)(n＋2)= 只写答案
1.1X2=1/3(1X2X3-0X1X2)2X3=1/3(2X3X4-1X2X3)3X4=1/3(3X4X5-2X3X4)将这三个等式的两边相加,可以得到1X2+2X3+3X4=(1/3)X3X4X5请计算：1X2X3+2X3X4+…n(n+1)(n+2).