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If f is a function satisfying f(x+y)=f(x...

If `f` is a function satisfying `f(x+y)=f(x)xxf(y)` for all `x ,y in N` such that `f(1)=3` and `sum_(x=1)^nf(x)=120 ,` find the value of `n` .

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To solve the problem, we will follow these steps: 1. **Understand the function**: We are given that \( f(x+y) = f(x) \cdot f(y) \) for all \( x, y \in \mathbb{N} \) and \( f(1) = 3 \). 2. **Calculate \( f(2) \)**: - Let \( x = 1 \) and \( y = 1 \): \[ f(2) = f(1+1) = f(1) \cdot f(1) = 3 \cdot 3 = 9 ...
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