Use the Root or Ratio Test for these problems. If those tests are inconclusive, only then use some other

$4$ of $4$ method to determine if the series converges or diverges.

Determine if the series ${\displaystyle \underset{n=2}{\overset{}{}}}\frac{n2}{2n3}$ converges or diverges.

Determine if the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{\sqrt[\phantom{2}]{n}}$ converges or diverges.

Determine if the series ${\displaystyle \underset{n=1}{\overset{}{}}}(\frac{1}{2}{)}^n$ converges or diverges.

$120$ MATH $166$: CALCULUS II NOTES

$4.$ Determine if the series ${\displaystyle \underset{n=2}{\overset{}{}}}(\frac{1}{nlnn}{)}^n$ converges or diverges.