Hey medos.

In this kind of problems you assuming something is true for n = k and then show its true for n = k + 1. This has a domino effect in that if its true for k=1 then its true for k = 2, but if its true for k=2 then its true for k= 3 and so on.

So what you have is Sum {k=1 to n} (1/SQRT(k)) < SQRT(n) but the sum of k+1 just adds 1/SQRT(k+1) so you have to prove that if that sum is less than SQRT(n) then the sum plus 1/SQRT(k+1) < SQRT(n+1) so If you can show that 1/SQRT(k+1) < SQRT(n+1) - SQRT(n) you're done.

It is a little tricky if you haven't seen it before.