# The Series of Madness

Algebra Level 5

$\large { \begin{eqnarray} A&=& \sum_{n=1}^{50} \left(x^n+\frac1{x^n} \right) \\ B&=&\sum_{n=1}^{10} \left(x^{5n-2}+\frac1{x^{5n-2}} \right) \end{eqnarray}}$

Given that $$x + \frac1x =4$$, with $$A$$ and $$B$$ as described above, find the value of $$\dfrac AB$$.

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