RU-ALLRUSSIAN 1968 Problem 7

The sequence $\mathrm{a}_{\mathrm{n}}$ is defined as follows: $\mathrm{a}_{1} = 1$ , $\mathrm{a}_{\mathrm{n} + 1} = \mathrm{a}_{\mathrm{n}} + 1 / \mathrm{a}_{\mathrm{n}}$ for $\mathrm{n} \geq 1$ . Prove that $\mathrm{a}_{100} > 14$ .