# trying to prove or disprove $C$ for the sequence: $\forall c \in N : S_n = n^2 - n$

The following shows the question I am working on.

However, I have no idea where to begin

The point here is that the choice of $$m$$ comes at the very end. We can always choose $$m=\frac {k^{165}+165} {S_k}$$ so that the inequality holds. [ We can take $$i=1$$]. Hence $$C$$ is true.