Romanian District Olympiad
Source: Grade XI
March 17, 2010
limitcalculuscalculus computations
Problem Statement
Prove that exists sequences with a_n\in \{\minus{}1,\plus{}1\}, for any , such that:
\lim_{n\rightarrow \infty}\left(\sqrt{n\plus{}a_1}\plus{}\sqrt{n\plus{}a_2}\plus{}...\plus{}\sqrt{n\plus{}a_n}\minus{}n\sqrt{n\plus{}a_0}\right)\equal{}\frac{1}{2}