Juxtaposing sum

Calculus Level 3

If one of the two series below is equal to 2, what is the value of the other one?

\[\begin{cases} 1 + x + x^2 + x^3 + \cdots \\\\ x + 2x^2 + 3x^3 + 4x^4 + \cdots \end{cases} \]

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