$(16$ points$)$ Find the interval $of$ convergence $of$ the power series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(-1{)}^n(x+1{)}^n}{\sqrt[\phantom{2}]{n}*2^n}.$ Remember

$to$ test the endpoints. For each test you use, name the test and show all your work applying the

test.