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**Rist** Hi again. I really need full solutions of the following, because it seems that my ways of solving are wrong or just too short.

1) Find the sum of the series. Posted it before, but I just didn't understand how to continue mr fantastic's solution and also I don't know anything about gamma-function, which Krizalid used in his solution. Anwser is 1-ln2, by the way.

$\displaystyle \sum_{n=1}^{\infty}\frac{6^n}{n(n+1)x^n}$

2) Check if series is convergent. I know that it does not converge but can't prove it.

$\displaystyle \sum_{n=3}^{\infty}\frac{n+1}{\sqrt[3]{n^4}\ln^4(n+1)}$

3) Find all the values of x for which the series converges. By my way of solving itm the answer is $\displaystyle x\in[-3;3)$

$\displaystyle \sum_{n=2}^{\infty}n^4\bigg(\frac{x^3n+4}{27n+\sin (2n)}\bigg)^n$