${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{w^2\sqrt[\phantom{2}]{4w^2+1}}dw$

Determine whether the series is convergent or divergent and circle the corresponding answer. Then write the test that allows one to determine convergence or divergence.

$($a$){\displaystyle \underset{i=1}{\overset{}{}}}\frac{1}{\sqrt[4]{i^3}}$

converge

diverge

Test:

$($b$){\displaystyle \underset{j=1}{\overset{}{}}}\frac{(-1{)}^j(j+1)}{j^2-3}$

converge

diverge

Test:

$($c$){\displaystyle \underset{k=1}{\overset{}{}}}cos(\frac{5}{k})$

converge

diverge

Test:

$($d$){\displaystyle \underset{m=1}{\overset{}{}}}\frac{m^2+5}{(m+2)!}$

converge

diverge

Test: