Suppose \( \alpha \) and \( \beta \) are the roots of the quadratic equation associated with the infinite series \( x, \frac{x(x-2)}{x+1}, \frac{x(x-2)^2}{(x+1)^2}, \dots \). For what values of \( x \) will this series have a sum to infinity?
University of Ilorin MTH101 2025A past question
- a. \( \left| \frac{x-2}{x+1} \right| \leq 1 \)
- b. \( x < 1 \)
- c. \( \left| \frac{x-2}{x+1} \right| < 1 \)
- d. \( \left| \frac{x(x-2)}{x+1} \right| < 1 \)
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