# When a Rectangle and Cube are Summed!

Algebra Level 3

Let $$f(n) = \dfrac{g(n)}{h(n)}$$, where $$g(n) = 1^3 + 2^3 + \cdots + n^3$$ and $$h(n) = 2 + 6 + 12 + 20 + 30 + \cdots + n(n+1)$$.

If the value of $$f(100)$$ can be expressed as $$\dfrac mn$$, where $$m$$ and $$n$$ are coprime positive integers, find $$m+n$$.

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