Question

The sum of infinite series $\left| \begin{matrix} 1 & 2 \\ 6 & 4 \end{matrix} \right|$ + $\left| \begin{matrix} 1/2 & 2 \\ 2 & 4 \end{matrix} \right|$ + $\left| \begin{matrix} 1/4 & 2 \\ 2/3 & 4 \end{matrix} \right|$ + ….. is –

• A. – 10
• B. 0
• C. 10
• D. ∞

Answer 1

Answer: (A)

– 10

Answer 2

$\left| \begin{matrix} 1 + 1/2 + 1/4 + .....\infty & 2 \\ 6 + 2 + 2/3 + ......\infty & 4 \end{matrix} \right|$ = $\left| \begin{matrix} \frac{1}{1–\frac{1}{2}} & 2 \\ \frac{6}{1–\frac{2}{3}} & 4 \end{matrix} \right|$= $\left| \begin{matrix} 2 & 2 \\ 9 & 4 \end{matrix} \right|$ = – 10