Qurstion# I

Use the Limit comparison test to determine whether ${\displaystyle \underset{m=11}{\overset{}{}}}{a}_n={\displaystyle \underset{m=1}{\overset{}{}}}\frac{8n3}{11n^{6}6}$ converge or diverge

Questlontt

Use the ratio test to determine given series ${\displaystyle \underset{n=13}{\overset{}{}}}\frac{n{7}^n}{(n2{)}^n}$ converge or diverge

Questionts

Find the interval and radius of comvergence of the power series ${\displaystyle \underset{k=3}{\overset{}{}}}\frac{2}{3^{k}k}(x-4{)}^k$

Queatian$44$ Does ${\displaystyle \underset{k=1}{\overset{}{}}}\frac{(-1{)}^k}{3\sqrt[\phantom{2}]{k}}$ converge conditionally, converge abwolutely, or diverge?

Explain completely showing all work for all nests you me

Questions $5$ Let $u=($:$1,A,-3$:$)$ and $v=($:$2,0,-1$:$).$

$($a$)$ Find a unit vector that peints in the same directions as $=-2v.$

$($b$)$ Are $v$ and v orthogonal? Explain.