Re: [級數] 三個相乘?

[Honor1984 (希望願望成真)]

※ 引述《anger50322 (江)》之銘言：
: (1/1‧2‧3)+(2/2‧3‧4)+(3/3‧4‧5)+......+[1/n(n+1)(n+2)]=n(n+3)/4(n+1)(n+2)
              ^^          ^^
               1           1

               1
左式 = Σ -----------
          k(k+1)(k+2)

             n   1         2         1
     = (1/2)Σ [---  -   ----   +  ----]
            k=1  k        k+1       k+2


     = (1/2)[ 1/1 - 1/2 - 1/(n+1) + 1/(n+2)]

        n(n+3)
     = --------
       4(n+1)(n+2)

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推 anger50322:非常感謝!!!!
→ yhliu       :1/[k(k+1)(k+2)]=(1/2){1/[k(k+1)]-1/[(k+1)(k+2)]}
→ yhliu       :加總式相消結果=(1/2){1/(1．2)-1/[(n+1)(n+2)]}