convergent and divergent sequences

[khadi]

if sequence a[n][/n] is convergent does that also mean the same sequence in absolute value bars is convergent as well? and vise versa?

 

[Steven G]

Which is bigger a_n or |a_n|?

 

[LCKurtz]

if sequence a[n][/n] is convergent does that also mean the same sequence in absolute value bars is convergent as well? and vise versa?

Because of the [MATH]\frac 1 n[/MATH] in there, I'm wondering if you meant series instead of sequence. Anyway, assuming you meant what you wrote, the answer is yes. If [MATH]b_n\to L[/MATH] then [MATH]|b_n|\to |L|[/MATH] because [MATH] |~ |b_n|-|L|~ | \le |b_n - L | \to 0[/MATH]. Think about [MATH](-1)^n[/MATH] for the vise-versa.