匿名使用者
匿名使用者 發問時間: 科學數學 · 3 年前

請問各位大大,這題該怎麼解?

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2 個解答

評分
  • 3 年前
    最佳解答

    Sol

    1+(1+2)+(1+2+3)+…+(1+2+3+…+n)

    =(1*2)/2+(2*3)/2+(3*4)/2+…+n(n+1)/2

    =(1/2)*Σ(k=1 to n)_k(k+1)

    =(1/2) Σ(k=1 to n)_k^2+(1/2) Σ(k=1 to n)_k

    =n(n+1)(2n+1)/12+n(n+1)/4

    =[n(n+1)/12]*[(2n+1)+3]

    =n(n+1)(n+2)/6

  • 3 年前

    1+(1+2)+(1+2+3)+···+(1+2+3+···+n)

    = (1×2 + 2×3 + 3×4 +...+ n(n+1))/2

    = (1×2(3-0) + 2×3(4-1) + 3×4(5-2) +...

    + n(n+1)(n+2 - (n-1)) )/6

    = (-0×1×2+1×2×3 - 1×2×3+2×3×4

    - 2×3×4+3×4×5 -...+ n(n+1)(n+2))/6

    = n(n+1)(n+2)/6

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