# 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 \(\dfrac AB\).