用最快的方法 和 不需計算器 來計算 (急)!!!

1+(1+2)+(1+2+3)+…+(1+2+3+…+30)=1*30+2*29+3*28+…+29*2+30*1=Σ(k=1 to 30)_k*(31－k)=31Σ(k=1 to 30)_k－Σ(k=1 to 30)_k^2=31*(30*31/2)－30*31*61/6=14415－9455=4960

2011-05-05 22:42:30 補充：
1+(1+2)+(1+2+3)+…+(1+2+3+…+30)
=Σ｛(k=1 to 30)_[Σ(w=1 to k)_w]｝
=Σ[(k=1 to 30)_k(k+1)/2]
=(1/2)Σ(k=1 to 30)_k^2+(1/2)Σ(k=1 to 30)_k
=30*31*61/12+30*31/4
=4727.5+232.5
=4960

∑ k(k+1)/2, k=1~30
=(1/2) ∑ k^2+k
=(1/2) [(30*31*61)/6+(30*31)/2]
=4960