I've to show whether the following infinite series converges or not. The problem is that I tried to prove it's divergent by induction, by the root test and by trying to bound it from below. But I couldn't reach any conclusion.
Here it comes : . I'm sure it's a famous one. It's very similar to the one that defines (inversed).
I'd like you to tell me what test should I try. Then if I'm not able to get a conclusion, I'll ask for further help. Thanks in advance.
My intuition fails! I thought that would have been much greater than . But from what I did, all seemed to show the contrary and I couldn't believe it.Or consider that for very large n we have that (high-light)
n!<<n^n by stirlings approximation
I was trying to show that if , then it would diverges. I recognized it was false, but I wouldn't trust my result!
Of course! Since , the series converges... Now I will try to prove it!