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Results tagged with infinite-sequences
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user 75491
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boundedness of a nonlinear recursive sequence
Consider a real sequence $(x_k)$ for $k=0,1,2,\dots,N$ as $x_0=1$ and for $k>0$
$$ x_k=x_{k-1}+\frac{\gamma}{N}x_{k-1}^2,\qquad (\gamma>0).$$
I wonder to show that the sequence is bounded as $N\to\inf …
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