Sir subconvex

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opincariumihai
Thales
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Sir subconvex

Post by opincariumihai »

Fie \( (x_n) \) un sir marginit si \( a\geq1 \) astfel incat \( x_{n+2}\leq(1-a)x_{n+1}+ax_n \). Aratati ca sirul este convergent.

Dan Marinescu
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Marius Mainea
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Post by Marius Mainea »

Daca \( a=1 \) nu merge.

Daca in enunt punem \( a>-1 \), \( a\neq 1 \), \( x_{n+2}\le (1+a)x_{n+1}-ax_n \) si \( (x_n) \) marginit, atunci merge.
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opincariumihai
Thales
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Post by opincariumihai »

Banuiesc ca ar fi fost corect \( a<1 \).
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