can someone explain this proof to me?

theorem:

let sn be a convergent seq with sn -> l as n tends to infintiy. then every sunseq pf sn converges to l.

from my notes, it states that by induction, you can easily establise that nk > k for all k....

sorry, im new to the whole idea of proofs so im not sure how do i use induction to prove that nk > k..

thanks