08/01/03 18:17:12
>>19
20みたいにアタマ使わなくても
Σ[1≦i＜j＜k≦n]ijk
＝Σ[k=3,n]Σ[j=2,k-1]Σ[i=1,j-1]ijk
＝Σ[k=3,n]kΣ[j=2,k-1]jΣ[i=1,j-1]i
＝Σ[k=3,n]kΣ[j=2,k-1]j{j(j-1)/2}
＝(1/2)Σ[k=3,n]kΣ[j=2,k-1]{(j+1)-1}j(j-1)
＝(1/2)Σ[k=3,n]kΣ[j=2,k-1]{(j+1)j(j-1) - j(j-1)}
＝(1/2)Σ[k=3,n]k{ (k+1)k(k-1)(k-2)/4 - k(k-1)(k-2)/3 }
＝(1/2)Σ[k=3,n]{ (k+2)(k+1)k(k-1)(k-2)/4 - (k+1)k(k-1)(k-2)*(5/6) + k(k-1)(k-2)/3 }
＝(1/2){(n+3)(n+2)(n+1)n(n-1)(n-2)/24-(n+2)(n+1)n(n-1)(n-2)/6 +(n+1)n(n-1)(n-2)/12}
＝(1/2)(n+1)n(n-1)(n-2){(n+3)(n+2)/24-(n+2)/6 +1/12}
＝(1/2)(n+1)n(n-1)(n-2){n(n+1)/24}
＝{(n+1)^2}(n^2)(n-1)(n-2)/48
ってやればアホでもできるよ。