for part a, if then as you said , but then by definition and you have an increasing monotone series. if it was bounded by one, it would converge. and then you can take 2 elements close enough the the convergence point and show that the next point is above it.
if the series converge to x then you'll have , so x=4 or x=0.
you showed in part b something about the distance of the elements of the series from 4. if you can show this approaches to zero as n goes to infinity, then the series converges to 4.