# Questions tagged [divergent-series]

Questions on whether certain series diverge, and how to deal with divergent series using summation methods such as Ramanujan summation and others.

1,605 questions
Filter by
Sorted by
Tagged with
50 views

### Test for the convergence of the series $1/5 + 2!/5^2 + 3!/5^3+\ldots$

The series is $1/5 + 2!/5^2 + 3!/5^3+\ldots$ It's $n$th term will be $n!/5^n$ The problem I'm facing that I'm getting infinity using D'Alembert's ratio test.
47 views

### Series Test, Calculus 2 [closed]

I want to determine whether the series $$\sum_{n=3}^{\infty} \frac{1}{\ln(\ln(n))}$$ converges or diverges, and I don't know what test I should use. Thank you.
29 views

63 views

### Does this series converge or not?

$$\sum _{k=2}^{\infty }\:\frac{1}{\sqrt{k}\left(\ln k\right)^{\ln k}}$$ I've tried limit comparison with $\frac{1}{\sqrt{n}}$ and $\frac{1}{n^2}$ and also Cauchy condensation test but nothing seems to ...
### How does the divergent sum $\sum_{n=1}^\infty\cos(2n\gamma)\sin(2nt)$ correctly evaluate an integral? Surely distributions don’t apply here
$\newcommand{\d}{\,\mathrm{d}}\newcommand{\res}{\operatorname{Res}}$Note: I don’t know any distribution theory myself, but I was informed by someone else and hinted to by this answer that my problem ...