AP EAMCET · Maths · Determinants
\(\left|\begin{array}{ll}2 & 1 \\ 3 & 1\end{array}\right|+\left|\begin{array}{cc}1 & 1 / 3 \\ 3 & 1\end{array}\right|+\left|\begin{array}{cc}1 / 2 & 1 / 9 \\ 3 & 1\end{array}\right|+\left|\begin{array}{cc}1 / 4 & 1 / 27 \\ 3 & 1\end{array}\right|+\ldots \infty=\)
- A \(0\)
- B \(\frac{1}{2}\)
- C \(-\frac{1}{2}\)
- D \(-1\)
Answer & Solution
Correct Answer
(C) \(-\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\( T_n = \left| \begin{array}{cc} 2(1/2)^n & (1/3)^n \\ 3 & 1 \end{array} \right| = 2(1/2)^n - 3(1/3)^n \) \( S = \sum_{n=0}^{\infty} (2(1/2)^n - 3(1/3)^n) = \sum_{n=0}^{\infty} 2(1/2)^n - \sum_{n=0}^{\infty} 3(1/3)^n \) \( S = \frac{2}{1 - 1/2} - \frac{3}{1 - 1/3} \)…
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