Question

观察下列等式,得结论.(题目在里面)!

Answer 1

1*2*3*4+1=25=5^2 ,5^2 =（1*4+1）^2

2*3*4*5+1=121=11^2 ,11^2=(2*5+1)^2

3*4*5*6+1=361=19^2 ,19^2=(3*6+1)^2

4*5*6*7+1=841=29^2 ,29^2=(4*7+1)^2

设第一个数为n

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

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

应该是对的吧!嘿嘿