What kind of a sequence is this?

Calculus Level 3

\[1 + \dfrac{\frac89 (10^1 - 1)}{19^1} + \dfrac{\frac89 (10^2 - 1)}{19^2} + \dfrac{\frac89 (10^3 - 1)}{19^3} + \ldots = \ ? \]

Give your answer to three decimal places.

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