Answer
True
Work Step by Step
We're given the statement:
If \(\forall n \geq 1, \, a_{n+1} - a_n > 0\), then the sequence \(\{a_n\}\) is strictly increasing.
We're asked to determine whether the statement is true or false.
Let \(\{a_n\} = \{a_n\}_{n=1}^\infty\) be the sequence, and let \(f\) be a function such that the \(n\)th term in the sequence is \(a_n = f(n)\). We know that \(a_{n+1} > a_n\) for all \(n\), hence, we have that \(f(n) = a_n < a_{n+1} = f(n+1)\). Thus, \(f(n+1)>f(n)\), which means that the function is strictly increasing. Result: \[TRUE\]
