# Math Help - Absolute value of a sequence converges then . . .

1. ## Absolute value of a sequence converges then . . .

Question:
Prove or give a counterexample:
If the absolute value of a sequence is convergent then the sequence is convergent.

I think this is false, because it should be if the sequence is convergent, then the absolute value is convergent. I think a counterexample is (-1)^n as a counterexample. Does this sound right?

Thanks.

2. ## Re: Absolute value of a sequence converges then . . .

Originally Posted by CountingPenguins
Prove or give a counterexample:
If the absolute value of a sequence is convergent then the sequence is convergent. a counterexample is (-1)^n as a counterexample.
That is correct.