Sir convergent <=> primul termen satisface o conditie

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Tudorel Lupu
Euclid
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Joined: Mon Oct 01, 2007 8:58 pm
Location: Constanta

Sir convergent <=> primul termen satisface o conditie

Post by Tudorel Lupu »

Fie \( (x_{n})_{n\geq 1} \) un sir de numere reale strict pozitive astfel incat \( x_{1} \) este fixat si \( x_{n+1}^{n}=a\cdot x_{n}^{n+1},\forall n\geq 1 \) si \( a>0 \) este dat. Sa se arate ca sirul \( (x_{n})_{n\geq 1 \) este convergent daca si numai daca \( x_{1}\leq\frac{1}{a} \).

Dorin Arventiev, Olimpiada locala Constanta, 2008
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