Convergence sequence proof

Feb 2008
64
0
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 \(\displaystyle |a|\)
 
Jul 2009
555
298
Zürich
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: \(\displaystyle \big|b_n-|a|\big| = \big||a_n|-|a|\big|\leq |a_n-a|\longrightarrow 0\)