Series! Convergence or Divergence?

[kilroymcb]

Hello!

Once again, I'm puzzled by some homework problems and hope you can render some assistance.

I'm given Sum from N=1 to Infinity of (n^5 - n^4 + 7n^3 + 2)/(6n^6 - 7n^4 + 3n)
When I plug in for the upper limit, I get infinity/infinity... obviously, indeterminate form. I could use L'Hospital's all day on this thing and probably still end up 0 at the end.
What would be the best approach to finding out whether it converges or diverges? Limit Comparision? Integral rule?

Same question on this one:
Sum from k=2 to infinity of (5)/k(ln(k))^2
I notice I have a sum of the form number over k * k squared. I know that 1/n^2 converges and that the other exponents of that form diverge. How could I use this to solve the problem?

thanks to all even just for looking!

 

[pka]

For your first problem that series is comparable to \(\displaystyle \sum\limits_n {\frac{1}{n}}.\)

For your second problem consider the integral test.
\(\displaystyle \int\limits_2^\infty {\frac{{dx}}{{x\left[ {\ln \left( x \right)} \right]^2 }}} .\)