# Use Alternating Series Test

• Apr 24th 2010, 03:55 PM
iyoo
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?
• Apr 24th 2010, 06:12 PM
tonio
Quote:

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
• Apr 25th 2010, 03:32 AM
HallsofIvy
Quote:

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?

$\displaystyle "\sum |A_n|$ converges" is exactly what "absolute convergence" means!