观察下列等式1×2=1/3×1×2×31×2+2×3=1/3×2×3×41×2+2×3+3×4=1/3×3×4×51×2+2×3+3×4+4×5=1/3×4×5×6…………………………用带n的式子表示发现的规律thankyouverymuch

Question

观察下列等式
1×2=1/3×1×2×3
1×2+2×3=1/3×2×3×4
1×2+2×3+3×4=1/3×3×4×5
1×2+2×3+3×4+4×5=1/3×4×5×6
…………………………
用带n的式子表示发现的规律
thank you very much

Answer 1

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