# 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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