Determine convergence or divergence using the appropriate test

${\displaystyle \underset{n=1}{\overset{}{}}}sin(\frac{n}{2})$

Find the interval of convergence

${\displaystyle \underset{n=0}{\overset{}{}}}\frac{(-1{)}^n(x1{)}^n}{2^n}$

Use partial fractions to find the power series of

$\frac{4}{(x-3)(x1)}$