Can Integrating to Infinity Determine Convergence or Divergence of a Series?

[somebodyelse5]

Am I allowed to simply take the integral from n=# to infinity to determine if the series converges or diverges?

If the answer is infinity then it diverges
If the answer is a number then it converges, is the sum this number or does it converge to this number? Or is the number it converges to the same as the sum?

 

[wisvuze]

the terms must be decreasing and it will only tell you whether or not it converges or diverges

 

[Whitishcube]

Yes, you can do this. If you integrate the sequence in the series to infinity, the integral and the series do the same thing, diverge or converge. However, the sums are different values if they converge. The only problem is that most series encountered can't be integrated easily or at all.