Problem 272 (difficulty: 3/10)

Prove that if \(\displaystyle a_n\to a>0\) and \(\displaystyle (b_n)\) is an arbitrary sequence, then

\(\displaystyle \Ulim (a_n\cdot b_n) = a \cdot \Ulim b_n \quad\text{and}\quad \Olim (a_n\cdot b_n) = a \cdot \Olim b_n. \)

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