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Posted: **Tue Mar 18, 2008 12:05 pm**

Fie sirul \( (a_n) \) de numere reale astfel incat \( |a_m-a_n| <\frac{m}{n} \) pentru orice \( m,n \in \mathbb{N}^* \). Aratati ca sirul este constant.

C. Mortici, RMT 1/2008

Posted: **Mon Jun 09, 2008 5:26 pm**

\( |a_m-a_n|\leq|a_m-a_k|+|a_n-a_k|<\frac{m}{k}+\frac{n}{k} \longrightarrow0\ \ \(k\longrightarrow\infty) \)

mateforum.ro

Sir constant

Sir constant