Thread: determine whether the following series converge or diverge

Determine whether the following series converge or diverge:


(3n^4+6n^2-17)/(2n^6-9n^4+n+1). I compared it with (5/6)^n, which converges

5^n/n!. Converges by ratio test

1/l(og(n))^n converges by ratio test

(-1)^n/n^(1/3) converges by alternating series test since 1/n^(1/3) is a decreasing sequence which tends to 0


I'm a bit suspicious of my answers since I got that they all converge

Thanks in advance

Originally Posted by poirot

I'm a bit suspicious of my answers since I got that they all converge

(3n^4+6n^2-17)/(2n^6-9n^4+n+1). I compared it with (5/6)^n, which converges

5^n/n!. Converges by ratio test

1/l(og(n))^n converges by ratio test

(-1)^n/n^(1/3) converges by alternating series test since 1/n^(1/3) is a decreasing sequence which tends to 0

Thanks in advance

if and with for all then .
define . then . also . so

now

They are series not sequences and I just need to tell whether they converge or diverge. Thanks anyway.

Originally Posted by poirot

Determine whether the following series converge or diverge:


(3n^4+6n^2-17)/(2n^6-9n^4+n+1). I compared it with (5/6)^n, which converges

use the limit comparison test with the known convergent series 1/n^2

5^n/n!. Converges by ratio test

correct

1/l(og(n))^n converges by ratio test

correct, but try root test

(-1)^n/n^(1/3) converges by alternating series test since 1/n^(1/3) is a decreasing sequence which tends to 0

correct

...

Thanks for suggesting the root test. It reminds me of the ratio test in that if c<1 it converges. Anyway so I was correct they are converge?