$(2$pts ea$)$ Fill in the blank

a$.$ The series ${\displaystyle \underset{?}{\overset{?}{}}}(-1{)}^n{b}_n$ converges when two conditions are met. The first condition is: $$

The second condition is: $$

The name of this test is the: $$

b$.$ For the series ${\displaystyle \underset{?}{\overset{?}{}}}(-1{)}^n{b}_n,$ if you estimate the sum by ${\displaystyle \underset{k=0}{\overset{n}{}}}(-1{)}^k{b}_k,$ then your accuracy $($error$)$ is $$

c$.$ Let $\sqrt[n]{a_n}L.$ What condition on $L$ guarantees that ${\displaystyle \underset{?}{\overset{?}{}}}{a}_n$ converges? $$

d$.$ If a series ${\displaystyle \underset{?}{\overset{?}{}}}{a}_n$ converges but ${\displaystyle \underset{?}{\overset{?}{}}}|a_n|$ diverges then we say that ${\displaystyle \underset{?}{\overset{?}{}}}{a}_n$ converges $$

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Most of the following problems do not require as much space as I am giving you. Be sure to leave all attempts, even if they did not work. Draw a box around all work that is part of your final answer so that I can distinguish it$.$

$3.(8$pts$)$ Use the Integral Test to show that ${\displaystyle \underset{?}{\overset{?}{}}}\frac{1}{\sqrt[\phantom{2}]{n}}$ diverges. Be sure to establish that the conditions $($there are two$)$ of the test are met. And write out the improper integral carefully!