Ok so giving this a second try, for the first one,
using the root test, we end up with
(1 + (1/n)) * x,
so the limit is absolute value of x, which must be less than 1 to converge, so we set the equation
-1< x< 1
plugging -1 into x we get , (-1)^n * (1+(1/n))^n , a diverging alternating...