Let $\{a_n\}$ be a sequence with limit $\alpha$, and define $b_n=a_{n+1}$ where $n\in \mathbb{N}$. Show that $\{b_n\}\rightarrow \alpha$. Let $\{a_n\}$ be a sequence with limit $\alpha$, and define $b_n=a_{n+1}$ where $n\in \mathbb{N}$. Show that $\{b_n\}\rightarrow \alpha$.
What I have:
Since $\{a_n\}\rightarrow \alpha$ we know that for all $\epsilon>0$ there exists $N\in \mathbb{N}$ such that $|a_n-\alpha|<\epsilon$ for all $n\geq N$.
I'm stuck trying to figure the rest out. Any help is greatly appreciated, thank you.

Since $\{a_n\}\rightarrow \alpha$ we know that for all $\epsilon>0$ there exists $N_1\in \mathbb{N}$ such that $|a_n-\alpha|<\epsilon$ for all $n\geq N_1$. Let $N=N_1-1$. Then $\forall n\ge N$, $|b_n-\alpha|=|a_{n+1}-\alpha|<\epsilon$.
