Finding limit $\lim_{n\to\infty}\frac{x_1+x_2+\dots+x_n}{n}$

Asked Jun 10 '14 at 19:48

Active Jun 10 '14 at 19:51

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I don't know how to solve the following:

Let $(x_n)_{n=1}^\infty$ be a sequence with property $\sum_{n=1}^\infty |\frac{x_n}{n}|<\infty$. Find a limit $\lim_{n\to\infty}\frac{x_1+x_2+\dots+x_n}{n}$.

Any hint is welcome. Thanks in advance.

asked Jun 10 '14 at 19:48

alans

6,475

4

More general result – Daniel Fischer Jun 10 '14 at 19:50
Does $x$ have a range of values it can take on? Check out the law of large numbers as well – ClassicStyle Jun 10 '14 at 20:34

Finding limit $\lim_{n\to\infty}\frac{x_1+x_2+\dots+x_n}{n}$

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