Similar sums (corrected)

Algebra Level 4

\[\begin{align} S_1 & = \frac{1}{11}+\frac{111}{1111}+\frac{11111}{111111}+\cdots+ \frac {\overbrace {111...1}^{(2n-1)\times 1's}}{\underbrace{1111...1}_{2n \times 1's}} \\ S_2 & = \frac{1}{11}+\frac{1}{1111}+\frac{1}{111111}+\cdots+ \frac {1}{\underbrace{1111...1}_{2n \times 1's}} \end{align} \]

For \(S_1\) and \(S_2\) as defined above, find the value of \(\dfrac {2n+9(S_{2}-S_{1})}{S_{2}+S_{1}}\) for \(n=2017\).


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