1×2×3+2×3×4+3×4×5+…+n(n+1)(n+2)=?

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1×2×3+2×3×4+3×4×5+…+n(n+1)(n+2)=?1×2×3+2×3×4+3×4×5+…+n(n+1)(n+2)=?1×2×3+2×3×4+3×4×5+…+n(n+1)(n+2)=?1

1×2×3+2×3×4+3×4×5+…+n(n+1)(n+2)=?
1×2×3+2×3×4+3×4×5+…+n(n+1)(n+2)=?

1×2×3+2×3×4+3×4×5+…+n(n+1)(n+2)=?
1×2×3+2×3×4+3×4×5+.+n(n+1)(n+2)
=1/4【1×2×3×4-0×1×2×3】+1/4【2×3×4×5-1×2×3×4】+1/4【3×4×5×6-2×3×4×5】+.+
1/4【n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2)】
=1/4n(n+1)(n+2)(n+3)
希望对你能有所帮助.

1*2*3=1/4(1*2*3*(4-0)
2*3*4=1/4(2*3*4*(5-1)
......
n*(n+1)*(n+2)=1/4*n*(n+1)*(n+2)[n+3-(n-1)]
Sn=1*2*3+2*3*4+3*4*5+...+n*(n+1)*(n+2)
=1/4{1*2*3*(4-0)+2*3*4*(5-1)+3*4*5*(6-2)...+n*...

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1*2*3=1/4(1*2*3*(4-0)
2*3*4=1/4(2*3*4*(5-1)
......
n*(n+1)*(n+2)=1/4*n*(n+1)*(n+2)[n+3-(n-1)]
Sn=1*2*3+2*3*4+3*4*5+...+n*(n+1)*(n+2)
=1/4{1*2*3*(4-0)+2*3*4*(5-1)+3*4*5*(6-2)...+n*(n+1)*(n+2)[n+3-(n-1)]}
=1/4{1*2*3*4+2*3*4*5-1*2*3*4+3*4*5*6-2*3*4*5+..........+n*(n+1)(n+2)(n+3)-(n-1)*n(n+1)(n+2)}原式= n*(n+1)*(n+2)*(n+3)/4

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