Chủ đề này có 4 trả lời

[Dung Du Duong]

Cho dãy số $x_{n}$ như sau:

$x_{1}=12, x_{n+1}=\sqrt[n+1]{5x_{n}^{n}+2.7^{n}}, \forall n=1,2,3,... $

Xác định $x_{n}$

[huypham2811]

gt đề bài <=>

 

$x_{n+1}^{n+1}= 5x_{n}^{n}+2.7^{n}\Leftrightarrow x_{n+1}^{n+1}-7^{n+1}=5(x_{n}^{n}-7^{n})$

 

Suy ra ta có: $x_{n}^{n}-7^{n}=5^{n-1}.(x_{1}-7)$

 

Vậy ta có $x_{n}=\sqrt[n]{5^{n}+7^{n}}$

[khanghaxuan]

Try this : $x_{n+1}=\sqrt[n]{5x_{n}^{n}+2.7^{n}}$

[huypham2811]

Try this : $x_{n+1}=\sqrt[n]{5x_{n}^{n}+2.7^{n}}$

$x_{n+1}^{n} = 5.x_{n}^{n}+2.7^{n} \Leftrightarrow x_{n+1}^{n}+\frac{7^{n}}{2}=5(x_{n}^{n}+\frac{7^{n}}{2})$

 

suy ra $x_{n}^{n}+\frac{7^{n}}{2}=5^{n-1}(x_{1}^{n}+\frac{7^{n}}{2})$

 

Hay $x_{n}=\sqrt[n]{5^{n-1}(12^{n}+\frac{7^{n}}{2})-\frac{7^{n}}{2}}$

[khanghaxuan]

$x_{n+1}^{n} = 5.x_{n}^{n}+2.7^{n} \Leftrightarrow x_{n+1}^{n}+\frac{7^{n}}{2}=5(x_{n}^{n}+\frac{7^{n}}{2})$

 

suy ra $x_{n}^{n}+\frac{7^{n}}{2}=5^{n-1}(x_{1}^{n}+\frac{7^{n}}{2})$

 

Hay $x_{n}=\sqrt[n]{5^{n-1}(12^{n}+\frac{7^{n}}{2})-\frac{7^{n}}{2}}$

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