有一列等式:1×2×3×4+1=5^2=(1^2+3×1+1)^2 2×3×4×5+1=11^2=(2^2+3×2+1)^2 3×4×5×6+1=19^2=(3^2+3×3+1)^24×5×6×7+1=29^2=(4^2+3×4+1)^2……(1)根据你观察、归纳发现的规律,写出8×9×10×11+1的结果:_____(
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/12 04:55:09
![有一列等式:1×2×3×4+1=5^2=(1^2+3×1+1)^2 2×3×4×5+1=11^2=(2^2+3×2+1)^2 3×4×5×6+1=19^2=(3^2+3×3+1)^24×5×6×7+1=29^2=(4^2+3×4+1)^2……(1)根据你观察、归纳发现的规律,写出8×9×10×11+1的结果:_____(](/uploads/image/z/14835319-7-9.jpg?t=%E6%9C%89%E4%B8%80%E5%88%97%E7%AD%89%E5%BC%8F%3A1%C3%972%C3%973%C3%974%2B1%3D5%5E2%3D%281%5E2%2B3%C3%971%2B1%29%5E2+2%C3%973%C3%974%C3%975%2B1%3D11%5E2%3D%EF%BC%882%5E2%2B3%C3%972%2B1%EF%BC%89%5E2+3%C3%974%C3%975%C3%976%2B1%3D19%5E2%3D%EF%BC%883%5E2%2B3%C3%973%2B1%EF%BC%89%5E24%C3%975%C3%976%C3%977%2B1%3D29%5E2%3D%EF%BC%884%5E2%2B3%C3%974%2B1%EF%BC%89%5E2%E2%80%A6%E2%80%A6%EF%BC%881%EF%BC%89%E6%A0%B9%E6%8D%AE%E4%BD%A0%E8%A7%82%E5%AF%9F%E3%80%81%E5%BD%92%E7%BA%B3%E5%8F%91%E7%8E%B0%E7%9A%84%E8%A7%84%E5%BE%8B%2C%E5%86%99%E5%87%BA8%C3%979%C3%9710%C3%9711%2B1%E7%9A%84%E7%BB%93%E6%9E%9C%EF%BC%9A_____%EF%BC%88)
有一列等式:1×2×3×4+1=5^2=(1^2+3×1+1)^2 2×3×4×5+1=11^2=(2^2+3×2+1)^2 3×4×5×6+1=19^2=(3^2+3×3+1)^24×5×6×7+1=29^2=(4^2+3×4+1)^2……(1)根据你观察、归纳发现的规律,写出8×9×10×11+1的结果:_____(
有一列等式:
1×2×3×4+1=5^2=(1^2+3×1+1)^2
2×3×4×5+1=11^2=(2^2+3×2+1)^2
3×4×5×6+1=19^2=(3^2+3×3+1)^2
4×5×6×7+1=29^2=(4^2+3×4+1)^2
……
(1)根据你观察、归纳发现的规律,写出8×9×10×11+1的结果:_____
(2)试猜想n(n+1)(n+2)(n+3)+1是哪一个数(用n表示)的平方,并予以证明.
有一列等式:1×2×3×4+1=5^2=(1^2+3×1+1)^2 2×3×4×5+1=11^2=(2^2+3×2+1)^2 3×4×5×6+1=19^2=(3^2+3×3+1)^24×5×6×7+1=29^2=(4^2+3×4+1)^2……(1)根据你观察、归纳发现的规律,写出8×9×10×11+1的结果:_____(
(1)根据你观察、归纳发现的规律,写出8×9×10×11+1的结果:=89^2=(8^2+3×8+1)^2
(2)试猜想n(n+1)(n+2)(n+3)+1是哪一个数(用n表示)的平方,并予以证明
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