# Thread: Use Alternating Series Test

1. ## The Absolute Convergence Test

The absolute convergence test states,
If Summation Notation (n=1 to n=infinity) abs(An) converges, then summation notation (n=1 to infinity) An converges.

So if abs (An) converges, does An converges absolutely? or should I check again for absolute convergent?

2. Originally Posted by iyoo
The absolute convergence test states,
If Summation Notation (n=1 to n=infinity) abs(An) converges, then summation notation (n=1 to infinity) An converges.

So if abs (An) converges, does An converges absolutely? or should I check again for absolute convergent?

If Abs(A_n) converges (absolutely) and then it converges (without the "absolutely" and without the absolute value).

Tonio

3. Originally Posted by iyoo
The absolute convergence test states,
If Summation Notation (n=1 to n=infinity) abs(An) converges, then summation notation (n=1 to infinity) An converges.

So if abs (An) converges, does An converges absolutely? or should I check again for absolute convergent?
$"\sum |A_n|$ converges" is exactly what "absolute convergence" means!