How do I show that diverges? Also, how do I show that converges? If you're too lazy for a full response, I think that just naming a test would be enough for such a problem.
Any input would be greatly appreciated!
Thanks in advance!
How do I show that diverges? Also, how do I show that converges? If you're too lazy for a full response, I think that just naming a test would be enough for such a problem.
Any input would be greatly appreciated!
Thanks in advance!
For the first one, you can use comparison with an integral (note that ). (or Cauchy condensation test)
For the second one, convergence is very quick, so any basic test will work.
How do I show that diverges? Also, how do I show that converges? If you're too lazy for a full response, I think that just naming a test would be enough for such a problem.
Any input would be greatly appreciated!
Thanks in advance!
When I do the first one, I did it with a u substitution u = ln(n)
and my last step is 8/3 * lim t->inf ln(t) - ln(0) but I said ln(0) not ln(0.00000000000000000001...) which does not exist. So, what does that mean or did I do something wrong?
When I do the first one, I did it with a u substitution u = ln(n)
and my last step is 8/3 * lim t->inf ln(t) - ln(0) but I said ln(0) not ln(0.00000000000000000001...) which does not exist. So, what does that mean or did I do something wrong?
when you use a u-substution, you have:
let
so,
you can use the limits given to see that the integral diverges.. this has been done in the above post by DeMath
When I do the first one, I did it with a u substitution u = ln(n)
and my last step is 8/3 * lim t->inf ln(t) - ln(0) but I said ln(0) not ln(0.00000000000000000001...) which does not exist. So, what does that mean or did I do something wrong?