Suppose that the sequence $a_n$ converges to $L$. Define the sequence $m_n$ by $m_n = frac{(a_1 + a_2 + cdots + a_n)}{n}$. Prove that $m_n o L$.
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Step 1
Step 1: Since $a_n$ converges to $L$, we know that for any $\epsilon > 0$, there exists an $N$ such that for all $n > N$, $|a_n - L| < \epsilon$. Show more…
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