1. The problem is to prove a property of the sequence $u_n$ using mathematical induction, given that $u_n$ is strictly increasing. 2. The principle of mathematical induction involves two steps: - Base case: Verify the property for the initial term, usually $n=1$. - Inductive step: Assume the property holds for $n=k$, then prove it holds for $n=k+1$. 3. Since $u_n$ is strictly increasing, we know that for all $n$, $u_{n+1} > u_n$. 4. To prove a property $P(n)$ about $u_n$ by induction: - Show $P(1)$ is true. - Assume $P(k)$ is true for some $k \geq 1$. - Using the assumption and the fact that $u_n$ is strictly increasing, prove $P(k+1)$ is true. 5. This method leverages the monotonicity of $u_n$ to establish the property for all $n$. Final answer: Use induction starting from the base case and apply the strictly increasing property $u_{n+1} > u_n$ in the inductive step to prove the desired property for all $n$.