Well, I just need a little help in these... There are parts that I can't completely understand:

Find the complete interval of convergence for each series

1. $\displaystyle \sum_{n = 1}^{\infty} \frac{(-1)^{n + 1}(x + 5)^{2n}}{2n}$

For this one... All I could do was set up the limit for the ratio test:

$\displaystyle L = \lim_{n\to \infty} \left| \frac{(-1)^{n + 2}(x + 5)^{2n + 2}}{(2n + 2)} * \frac{2n}{(-1)^{n + 1}(x + 5)^{2n}}\right|$

2. $\displaystyle \sum_{n = 0}^{\infty} \frac{\ln{(n + 1)}x^n}{(n + 1)}$

For this one, I did a bit of work... But I need to know something:

$\displaystyle L = \lim_{n\to \infty} \left| \frac{ln(n + 2)x^{n + 1}}{(n + 2)} * \frac{(n + 1)}{ln(n + 1)x^n}\right|$

$\displaystyle = \lim_{n\to \infty} \left| \frac{ln(n+2)(n+1)x}{ln(n+1)(n + 2)}\right|$

$\displaystyle = |x|\lim_{n\to \infty} \left| \frac{(ln(n + 2))^{n + 1}}{(ln(n + 1))^{n + 2}}\right|$

This supposedly equals:

$\displaystyle L = |x|$

But I don't really know how the limit gets to 1.

Any help is appreciated.