Q$5),($a$)$ Determine if each of the following series are absolutely convergent. condiomalls convergent or divergent.

$($i$)$

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

$(5$ marks$)$

$($ii$)$

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{cos(n)}{n^4}$

$($b$)$ Find a power series representation for the function

$f(x)=\frac{1}{(1-x{)}^2}$

and determine its radius of convergence.

$(5$ marks$)$

$($c$)$ Giving your answer in summation notation, find the Taylor series for

$f(x)=e^{-x}$

about $x=-4.$

$(5$ marks$)$