Hello

Ok, I'll just sketch the proof for you.

n=1

Therefore true for n=1,assume n=k is true, that is,

Consider n=k+1

after a bit of simple algebra, you'll arrive at

since ,

But by the induction hypothesis.

so

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.