JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \(\alpha \) and \(\beta \) are the roots of the equation \(375x^2 -25x -2 = 0\), then \(\mathop {\lim }\limits_{n \to \infty } \,\sum\limits_{r = 1}^n {{\alpha ^r}} + \mathop {\lim }\limits_{n \to \infty } \,\sum\limits_{r = 1}^n {{\beta ^r}} \) is equal to
- A \(\frac{1}{{12}}\)
- B \(\frac{{29}}{{358}}\)
- C \(\frac{7}{{116}}\)
- D \(\frac{{21}}{{346}}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{{12}}\)
Step-by-step Solution
Detailed explanation
\(375 x^{2}-25 x-2=0\) \(\alpha+\beta=\frac{25}{375}, \alpha \beta=\frac{-2}{375}\) \(\Rightarrow\left(\alpha+\alpha^{2}+\ldots \text { upto infinite terms }\right)\) \(+\left(\beta+\beta^{2}+\ldots \ldots \text { upto infinite terms }\right)\)…
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