Hi all,

So I have a homework assignment that I was hoping to have clarified.

The first problem is:

$\displaystyle \sum_{k=8}^{\infty} \frac{4}{2+4k}$ (by the basic comparison test)

My idea is that $\displaystyle 0 \leq \frac{4}{2+4k} \leq \frac{4}{4k}$ which I assume you factor out the 4 and make it the harmonic series. If anyone could help on that one to either confirm that one or point me in the right direction that'd be awesome.

The second problem is:

$\displaystyle \sum_{k=6}^{\infty} \frac{k^3+2k+3}{k^4+2k^2+4}$ (by the limit comparison test)

I found it to be $\displaystyle \sum_{k=6}^{\infty}\frac{1}{k}$ by simply taking $\displaystyle \frac {k^3}{k^4}$ which is the harmonic series $\displaystyle \frac{1}{k}$.

However, I don't know if the tail end theorem would apply and it would diverge, or to compensate for the k=6, I would have to make series $\displaystyle \sum_{k=1}^{\infty} \frac{1}{k^6}$ which is a p-series that converges.

So, being stuck between those two (although I believe it's harmonic and diverges), any help is very much appreciated!

Thanks to anyone who does help with one (or both) of the problems!