# Fluctuating series!

Calculus Level 2

$\frac 1{503}, \ \frac 4{524}, \ \frac 9{581}, \ \frac {16}{692}, \ \ldots$

The above is the sequence $$\left\{u_n = \frac {n^2}{500 + 3n^3}\right\}$$ with $$n=1, 2, 3, 4, \ldots.$$

If the largest term of this sequence can be expressed as $$\dfrac ab$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

×