Solve X from equation and evaluate infinite geometric series

Apuntes

• Subtopic: Solving the Equation Given the equation: $$\frac{X^{X^X}}{X} = 3^{1 - \frac{1}{\sqrt[3]{\sqrt[3]{3}}}}$$ We need to solve for \( X \). • Subtopic: Calculating the Series Sum Once \( X \) is determined, we need to calculate the sum of the infinite geometric series: $$S = 1 + X + X^2 + X^3 + \ldots$$ The formula for the sum of an infinite geometric series is: $$S = \frac{1}{1 - X}$$ where \( |X| < 1 \). • Subtopic: Answer Options The possible answers for \( S \) are: A) \(\frac{3}{2}\) B) \(\frac{1}{2}\) C) 2 To find the correct answer, we need to determine the value of \( X \) from the given equation and then use it to calculate \( S \).