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GH from MO
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Let $m$ is anbe positive integer, and consider the recursion

$$x_{n+1}=\frac{1}{m+1-nx_n}$$$$x_{n+1}=\frac{1}{m+1-nx_n}.$$

Does the limit of $x_n$ exist?

I'm guessing the limit doesn't exists for any $m$.

enter image description here

$m$ is an positive integer,

$$x_{n+1}=\frac{1}{m+1-nx_n}$$

Does the limit of $x_n$ exist?

I'm guessing the limit doesn't exists for any $m$

enter image description here

Let $m$ be positive integer, and consider the recursion

$$x_{n+1}=\frac{1}{m+1-nx_n}.$$

Does the limit of $x_n$ exist?

I'm guessing the limit doesn't exists for any $m$.

enter image description here

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YCor
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Does the limit of $x_n$, defined by $x_{n+1}=1/(m+1-nx_n)$ exist?

m$m$ is an positive integer,

$$x_{n+1}=\frac{1}{m+1-nx_n}$$

Does the limit of $x_n$ exist?

I'm guessing the limit doesn't exists for any $m$

enter image description here

Does the limit of $x_n$ exist?

m is an positive integer,

$$x_{n+1}=\frac{1}{m+1-nx_n}$$

Does the limit of $x_n$ exist?

I'm guessing the limit doesn't exists for any $m$

enter image description here

Does the limit of $x_n$, defined by $x_{n+1}=1/(m+1-nx_n)$ exist?

$m$ is an positive integer,

$$x_{n+1}=\frac{1}{m+1-nx_n}$$

Does the limit of $x_n$ exist?

I'm guessing the limit doesn't exists for any $m$

enter image description here

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GH from MO
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math110
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