Problem
TxO Math Bowl 2024 - Individuals B - Problem 8
Let S : \mathbb{Z}^+ \to \mathbb{Z}^+ be a function such that:
S(x) = \sum_{n=1}^{60} n(1+x)^n
If 60^2 \cdot S(60) = a\left(b^b\right) + b, where b is maximized and a, b \in \mathbb{Z}^+, find \left\lfloor \frac{a+b}{10} \right\rfloor.
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