“n(n+1)(n+2)(n+3)+1”是哪个数的平方?

问题描述:

“n(n+1)(n+2)(n+3)+1”是哪个数的平方?
1个回答 分类:数学 2014-10-17

问题解答:

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答:
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
所以是n^2+3n+1的平方.
 
 
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