2. Relevant equations Prove the following for n > 1, n is a natural number. Sum (from i=1 to n) of: 1/sqrt(i) is > then sqrt(n) 3. The attempt at a solution To be honest I have spent 2+ hours on this with little results. I have tried induction on n, I tried showing one increases more every step then the other ie: A_n = Sum (from i=1 to n) of: 1/sqrt(i) B_n = sqrt(n) That A_(n+1) / A_n > B_(n+1) / B_n I have tried squaring both sides and simplifying the expression. I just cannot seem to make any progress on this. Any help would be appreciated.