# Convergence sequence proof

#### Stylis10

How would i go about proving this:

Let $$\displaystyle (a_n)$$ be a sequence convergent to the limit $$\displaystyle a \in \mathbb{R}$$. Prove that the sequence of absolute values $$\displaystyle (b_n)$$ with $$\displaystyle (b_n) = |a_n|$$ is convergent to the limit $$\displaystyle |a|$$

#### Failure

How would i go about proving this:

Let $$\displaystyle (a_n)$$ be a sequence convergent to the limit $$\displaystyle a \in \mathbb{R}$$. Prove that the sequence of absolute values $$\displaystyle (b_n)$$ with $$\displaystyle (b_n) = |a_n|$$ is convergent to the limit $$\displaystyle |a|$$
Hint: $$\displaystyle \big|b_n-|a|\big| = \big||a_n|-|a|\big|\leq |a_n-a|\longrightarrow 0$$