1×2×3×4+1=25=5² 2×3×4×5+1=121=11² 3×4×5×6+1=361=19

(n-1)*n*(n+1)*(n+2)+1
=n(n²-1)*(n+2)+1
=n(n³-n+2n²-2)+1
=n^4-n²+2n³-2n+1
=n^4+2n³+n²-2n²-2n+1
=n²(n+1)²-2n(n+1)+1
=[n(n+1)-1]²
=(n²+n-1)²
再问： 请说明其正确性！
再答： 根据题中的数据规律得出 (n-1)*n*(n+1)*(n+2)+1 =n(n²-1)*(n+2)+1 =n(n³-n+2n²-2)+1 =n^4-n²+2n³-2n+1 =n^4+2n³+n²-2n²-2n+1 =n²(n+1)²-2n(n+1)+1 =[n(n+1)-1]² =(n²+n-1)² 其中n>1 以上是推导步骤 可将数据带入以验证正确性 带入2得 1×2×3×4+1=5² 带入3得 2×3×4×5+1=11² 验证正确！