Find a power series for the following functions centered at $c$ and then determine the interval

of convergence.

$($a$)f(x)=\frac{3}{2-x},c=0$

$($b$)f(x)=\frac{3}{2-x},c=1$

$($c$)f(x)=\frac{5x+4}{x^2+x-2},c=0($Hint: Use partial fractions to rewrite$).$

$($d$)f(x)=\frac{1}{(x+1{)}^2},c=0($Hint: Note that $\{$:${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}f(x)dx=-\frac{1}{x+1})$