$(10$ points$)$ For each series, determine if it converges or diverges and give an explanation ${\displaystyle \underset{?}{\overset{?}{}}}$why. $,3(0\mathrm{.}8{)}^0=3,3(0\mathrm{.}8{)}^1=2\mathrm{.}4>>(0\mathrm{.}8{)}^2=1.{\displaystyle \underset{n=0}{\overset{}{}}}3(0\mathrm{.}8{)}^n$

$])$:$\})$:$\}$

${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^n*n^2$

$[uarr$

tirs jsist deturs

hathis it ic negre or porve gest frow $$ The seres convergs $\frac{1}{1-0\mathrm{.}1}$ use companison test

$\frac{1}{0\mathrm{.}4}=1\mathrm{.}1$

to shew because this

$\frac{1}{1000-0\mathrm{.}9}=944\mathrm{.}9$

logic is not enough to shaw divegerce