By the sequence $(x_n)_{n\in\Bbb{N}}$, define a new sequence $(t_n)_{n\in\Bbb{N}}$ such that $t_n:=\frac {x_1+x_2+...+x_n}{n}$. If $\lim_{n\rightarrow\infty}t_n=\omega$, how can I show that $\lim_{t\rightarrow\infty}x_n=\omega$?
Original post had ``If $\lim_{n\rightarrow\infty}x_n=\omega$, ..."