O problema cu siruri

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Marius Dragoi
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Joined: Thu Jan 31, 2008 5:57 pm
Location: Bucharest

O problema cu siruri

Post by Marius Dragoi »

Se considera sirul \( {(x_n)}_{n \geq 1} \) dat de relatia \( x_{n+1}=n+x_n^2 \), unde \( x_1=1 \). Demonstrati ca exista un numar real pozitiv \( k \) astfel incat \( \lim_{n\to\infty}\ \frac {x_n}{k^{2^n}}=1 \).
Politehnica University of Bucharest
The Faculty of Automatic Control and Computers
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