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1x2十2x3十3x4十……十10x11(写出过程)

1×2+2×3+3×4+...+n×(n+1) = (1/3)×[1×2×3 - 0×1×2] +(1/3)×[2×3×4 - 1×2×3] +(1/3)×[3×4×5 - 2×3×4] +... +(1/3)×[n×(n+1)×(n+2) - (n-1)×n×(n+1)] = (1/3)×n×(n+1)×(n+2) [2] 相邻三个正整数乘积和 1×2×3+2×3×4+3×4×5+...+n×(n+1)×...

1x2+2x3+3x4+…+n(n+1) =1x(1+1)+2x(2+1)+3x(3+1)+…n(n+1) =(1^2+2^2+3^2+…+n^2)+(1+2+3+…+n) =n(n+1)(2n+1)/6+n(n+1)/2 =n(n+1)[(2n+1)+3]/6 1x2+2x3+3x4+…+10x11 =10x(10+1)x[(10x2+1)+3]/6 =110x4 =440

1x2+2x3+3x4+4x5+……+n(n+1) =1²+2²+3²+...........+n²+(1+2+3+.....+n) =n(n+1)(2n+1)/6+n(n+1)/2 =n(n+1)(n+2)/3 1x2+2x3+3x4+4x5+……+10x11 =10×11×12/3 =440

1x2x3x4x5x6x7x8x9x10x11÷(27X25X24X22) =(3×9÷27)×(5×10÷25)×(4×6÷24)×(2×11÷22)×7×8 =1×2×1×1×56 =112

原式=[1×(2×11)×(3×9)×(4×6)×7×8×(5×5)×2]÷(27×25×24×22)=(22×27×24×25×7×8×2)÷(22×27×24×25)=(22÷22)×(27÷27)×(24÷24)×(25÷25)×7×8×2=112

1X2+2X3X4+3X4X5X6+......+10X11X12X13......X20的末位数 与 1X2+2X3X4=26的末位数相同 末尾数为6

100的阶乘=9.33262154 × 10^157 1乘到100就是100的阶乘,数学符号是:100!具体得数是:9.332621544394415268169923885626e+157(e+157指10的157次幂),用计算器中的阶乘算最快。 详细的算法··· 1x2x3x4x5x6x7x8x9x10x11x12x13x14x15x16x17x18x...

因为这个式子的每一项都是1/n(n+1)的形式。 且1/n(n+1)=[(n+1)-n]/n(n+1)=1/n-1/(n+1) 所以原式=(1-1/2)+(1/2-1/3)+……+(1/10-1/11) =1+(-1/2+1/2-1/3+……+1/10)-1/11,括号内都相互抵消 =1-1/11 =10/11

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