1×2×3+2×3×4+...+∩(∩+1)(∩+2)

2024-12-17 04:53:24
推荐回答(1个)
回答1:

An=n(n+1)(n+2)=n³+3n²+2n
Sn=A1+A2+A3+…An
=(1³+3×1²+2×1)+(2³+3×2²+2×2)+(3³+3×3²+2×3)+…(n³+3n²+2n)
=(1³+2³+3³+…n³﹚+3×﹙1²+2²+3²+…n²﹚+2×﹙1+2+3+…n﹚
=[n(n+1)/2]²+3×[n(n+1)(2n+1)]/6 +[n﹙n+1﹚]∕2