The first one is rather simple just use the ratio test and prove that the limit of the sequence is <1 for -4<x<4

For part 2 of the question I first identified any similar series, I do this because if u find any similar series using the comparison test is really simple. The harmonic series was really similar to the series and by comparison test the series diverge.

For part 3 of the question, there is (-1)^n in the equation of the series. This normally indicates that using the alternating series test is normally the way to prove for convergence or divergence and it was the case for this question.