Ok, I'll just sketch the proof for you.
Therefore true for n=1, assume n=k is true, that is,
after a bit of simple algebra, you'll arrive at
But by the induction hypothesis.
Therefore, if n=k is true, then n=k+1 is true. But since n=1 is true, this implies than n=2 is true, which implies n=3 is true..etc. Hence for all natural numbers n, which, by definition, implies that 100 is an upper bound.