Sn= C^{1/n} so S1= C, S2= C^{1/2}, S3= C^{1/3}. etc. The first thing you are asked to show is that Sn> 1 for all n. Can you show that?

Then you are asked to show that S(n+1)< Sn, that is, that the sequence is decreasing- and there is a hint that you use proof by contradiction. Suppose that for some n, S(n+1)>= Sn so that C^{1/(n+1)}>= C^{1/n}. Since these are positive numbers, taking the n+ 1 power of each side won't change the direction of the inequality: C>= C^(n+1)/n= C(C^{1/n}. Why is that a contradiction.

Suppose that the limit, r, is less than 1. Let epsilon= 1- r. Then there exist N such that if n> N, |Sn- r|< epsilon (if you don't see why you are in the wrong class) so that Sn- r< 1- r giving Sn< 1, contradicting the very first thing you were to show.