Question

The value of $\begin{vmatrix}2 & 3 \\ 3 & 7\end{vmatrix}+\begin{vmatrix}1 & 2 \\ 3 & 7\end{vmatrix}+\begin{vmatrix}\frac{1}{2} & \frac{4}{3} \\ 3 & 7\end{vmatrix}+\begin{vmatrix}\frac{1}{2^2} & \frac{8}{3^2} \\ 3 & 7\end{vmatrix}+\ldots \ldots \infty$ is equal to

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

Answer 1

Answer: (D)

$\begin{vmatrix}2+1+\frac{1}{2}+\frac{1}{2^2}+\ldots \ldots \infty & 3+2+\frac{4}{3}+\ldots \ldots \infty \\ 3 & 7\end{vmatrix}=\begin{vmatrix}\frac{2}{1-\frac{1}{2}} & \frac{3}{1-\frac{2}{3}} \\ 3 & 7\end{vmatrix}$
$=\begin{vmatrix}4 & 9 \\ 3 & 7\end{vmatrix}=28-27=1$