0×1×2×3+1=1=1²；1×2×3×4+1=25=5²；2×3×4×5+1=121=11²；3_数学解答

0×1×2×3+1=1=1²；1×2×3×4+1=25=5²；2×3×4×5+1=121=11²；
3×4×5×6+1=261=19².可以发现规律是?
用字母表示

人气：285 ℃　时间：2019-10-17 02:55:04

解答

(n^2+3n+1)^2
n(n+1)(n+2)(n+3)+1=(n^2+3n+1)^2
n(n+1)(n+2)(n+3)+1
=[n(n+3)][(n+1)(n+2)]+1
=(n^2+3n)(n^2+3n+2)+1
=(n^2+3n)^2+2(n^2+3n)+1
=(n^2+3n+1)^2