What series test would you use on these and why? I just started learning series , I am trying to put everything together...I have few some few random problems just to see what kind of strategy you would use here...


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*$\displaystyle\sum_{n=1}^\infty\frac{n^n}{(2^n)^2}$

*$\displaystyle\sum_{n=1}^\infty\frac2{(2n - 1)(2n + 1)}$;  telescoping series ?

*$\displaystyle\sum_{n=1}^\infty\frac1{n(1 + \ln^2 n)}$

*$\displaystyle\sum_{n=1}^\infty\frac1{\sqrt{n (n + 1)}}$;   integral test ? cause you could do u-sub?

General and mixed hints:
$$\frac{2}{(2n-1)(2n+1)}=\left(\frac{1}{2n-1}-\frac{1}{2n+1}\right)$$
$$\frac{n}{4}\xrightarrow[n\to\infty]{}\infty$$
$$\frac{2^n}{2^n(1+n^2\log^22)}\le\frac{1}{\log^22}\cdot\frac{1}{n^2}$$
