the second one by root test
limit is 3>1 so the series diverge the first one sorry I do not know how to decide yet ..
Hello, I have been looking around for how to solve these to series by the integral test.
Problem 1 Evaluate
∞
Σ (n^(1/n))/n^3
n=1
decide if the series converges or diverges?
And,
Problem 2 Evaluate
∞
Σ (3^n*n!)/(3k)!
n=1
decide if the series converges or diverges?
First question - why on earth would you want to use the integral test (remember, you will need to integrate).
I would personally use a limit comparison test for the first. Compare with
for the second (it looks a little fishy) but
which clearly diverges - the terms don't go to zero.