Part I: Use the test indicated to determine if the series converges or diverges.

Note: ${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n=\underset{n}{lim}{S}_n=S$

$S_n=ln(\frac{1}{n}{)}^{\frac{1}{n}}$

${\displaystyle \underset{k=1}{\overset{n}{}}}(-1{)}^k(\frac{k}{2k1})$

Test: Limit of $a_n$

Test: Alternating series.

$3.{\displaystyle \underset{k=1}{\overset{n}{}}}\frac{14^k}{15^k}$

$4.S_n=nln(1\frac{1}{n})$

Test: Your choice.

Test: Your choice.

$5.{\displaystyle \underset{k=1}{\overset{n}{}}}(-1{)}^k(\frac{1}{k1})$

$6.{\displaystyle \underset{k=1}{\overset{n}{}}}\frac{1}{k^{2}3k2}$

Test: Alternating Series.

Test: Integral test.