For this particular proof I'm writing I'm relying on the fact that, for all , , the sequence is divergent. Of course, the result is intuitive and obvious, but in the problem statement I've been asked to prove separately any supporting claims such as this one. So, given that the claim is quite trivial, would it be sufficient just to proceed along the lines of:

"For all , , we have . Thus, taking , we have

Hence is divergent."

Or should I set about trying to prove this more rigorously using the definition of a limit of a sequence?