当n为任意实数,k为某一特定整数时,等式n(n+1)(n+2)(n+3)+l=(n2+kn+1)2成立.则k=______.
题型:填空题难度:一般来源:不详
当n为任意实数,k为某一特定整数时,等式n(n+1)(n+2)(n+3)+l=(n2+kn+1)2成立.则k=______. |
答案
n(n+1)(n+2)(n+3)+l, =(n2+3n)(n2+3n+2)+l, =(n2+3n)2+2(n2+3n)+l, =(n2+3n+1)2, ∵(n2+kn+1)2=(n2+3n+1)2, ∴k=3, 故答案为:3. |
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