Absolute Value of Limits Proof

[tnocel1]

Homework Statement

Show that if b_n→b, then the sequence of absolute values |b_n| converges to |b|.

Homework Equations

The Attempt at a Solution

I've been proving various properties of limits, including product of limits and sum of products, but have been having trouble making progress with the approach to absolute value of limits. I was also wondering is the converse of this is true, that is if |b_n|→|b|, is it also true that (b_n)→b

 

[susskind_leon]

Not at all, for example |(-1)^n| -> 1, but (-1)^n doesn't converge at all!
How about you start by writing down formally the assumption and what you want to prove. You will see that it's pretty straight forward then.