1 + 1/2 + 1/3 + ... + 1/n > 2n/n+1
where n > 2
For the base case let n=2.
So which is true so the base case holds
Now we'll assume the statement is true for n and consider it for n+1
(this is an analysis via cross multiplication)
And since 5n>4n for all n, so the statement is proven by induction