# Math Help - Converge 61.13

1. ## Converge 61.13

Prove: If lim xn = L as (n approaches infinity) the lim abs(xn) = L. (Hint: The inequality abs(abs(a) - abs(b)) is less than equal to abs(a-b).

abs= absolute value

2. well, they gave you the solution.

we have $|x_n-L|<\epsilon,$ and $||x_n|-|L||\le|x_n-L|$ so we're done.

3. Originally Posted by tigergirl
Prove: If lim xn = L as (n approaches infinity) the lim abs(xn) = L. (Hint: The inequality abs(abs(a) - abs(b)) is less than equal to abs(a-b).

abs= absolute value
Are you told that $L\ge 0$? If not, you can't prove it, it isn't true! What is true in general is that is [math\lim x_n= L[/tex] then $\lim |x_n|= |L|$.