An algebra problem by Saurabh Patil

Algebra Level 4

\[ \dfrac{2 + 6}{4^{100}} + \dfrac{2 + 2(6)}{4^{99}} + \dfrac{2 + 3(6)}{4^{98}} + \cdots + \dfrac{2 + 99(6)}{4^{2}} + \dfrac{2 + 100(6)}{4} \]

Let \(S\) denote the value of the expression above. Find \(3S\).

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