Question 70
Let $\mathbb{Z}^+$ be the set of positive integers. Find all strictly increasing functions $\mathbb{Z}^+ \to \mathbb{Z}^+$ with $f(1) = 1$ that satisfy the equation
$$
3 \cdot (f(1) + f(2) + \dots + f(n)) = f(n+1) + f(n+2) + \dots + f(2n)
$$
for all $n \in \mathbb{Z}^+$.
$$
3 \cdot (f(1) + f(2) + \dots + f(n)) = f(n+1) + f(n+2) + \dots + f(2n)
$$
for all $n \in \mathbb{Z}^+$.