(n+1）(n+2)(n+3)(n+4)+1=（)( )

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(n+1）(n+2)(n+3)(n+4)+1=（)( )
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(n+1）(n+2)(n+3)(n+4)+1=（)( )
(n+1）(n+2)(n+3)(n+4)+1=（)( )

(n+1）(n+2)(n+3)(n+4)+1=（)( )
(n+1)(n+2)(n+3)(n+4)+1=[(n+1)(n+4)][(n+2)(n+3)]+1
=(n^2+5n+4)(n^2+5n+6)+1
令:u=n^2+5n
则原式=(u+4)(u+6)+1
=u^2+10u+24+1
=(u+5)^2
所以:
原式=(n^2+5n+5)^2

(n+1)(n+2)(n+3)(n+4)+1=(n+1)(n+4)(n+2)(n+3)+1=(n²+5n+4)(n²+5n+6)+1=(n²+5n)²+10(n²+5n)+24+1=(n²+5n)²+10(n²+5n)+25=(n²+5n+5)(n²+5n+5)