Question

The value of $\left|\begin{array}{cc}2& 3\\ 3& 7\end{array}\right|+\left|\begin{array}{cc}1& 2\\ 3& 7\end{array}\right|+\left|\begin{array}{cc}\frac{1}{2}& \frac{4}{3}\\ 3& 7\end{array}\right|+\left|\begin{array}{cc}\frac{1}{2^2}& \frac{8}{3^2}\\ 3& 7\end{array}\right|+\dots \dots \infty$ is equal to

• A. 13
• B. 5
• C. $\frac{-13}{2}$
• D. 1

Answer 1

Answer: (D)

$\left|\begin{array}{cc}2+1+\frac{1}{2}+\frac{1}{2^2}+\dots \dots \infty & 3+2+\frac{4}{3}+\dots \dots \infty \\ 3& 7\end{array}\right|=\left|\begin{array}{cc}\frac{2}{1-\frac{1}{2}}& \frac{3}{1-\frac{2}{3}}\\ 3& 7\end{array}\right|$
$=\left|\begin{array}{cc}4& 9\\ 3& 7\end{array}\right|=28-27=1$