Repunits

Algebra Level 3

A repunit is a number that contains only the digit 1, and the repunit of \(n\) digits is denoted by \(R_{n} = \underbrace{11111 \ldots 1}_{n \text{ times}} \).

If \(f(x) = 90x^2 + 20x + 1\), then find the sum of digits of the number \(f(R_{10})\).

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