prove by induction that $1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + ... +\frac{1}{\sqrt{n}} \leq 2\sqrt{n} - 1$
Prove inequalities $2\sqrt{n+1}-2 \leq 1 + 1/\sqrt{2} + 1/\sqrt{3} + .... + 1/\sqrt{n}\leq 2\sqrt{n}-1$