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 $\displaystyle L\ge 0$? 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 $\displaystyle \lim |x_n|= |L|$.