Question

The sum of infinite series $\left|\begin{array}{cc}1& 2\\ 6& 4\end{array}\right|+\left|\begin{array}{cc}\frac{1}{2}& 2\\ 2& 4\end{array}\right|+\left|\begin{array}{cc}\frac{1}{4}& 2\\ \frac{2}{3}& 4\end{array}\right|+$ ....... is

• A. $-10$
• B. $0$
• C. $10$
• D. $\infty$

Answer 1

The correct option is A $-10$

$\left|\begin{array}{cc}1& 2\\ 6& 4\end{array}\right|+\left|\begin{array}{cc}\frac{1}{2}& 2\\ 2& 4\end{array}\right|+\left|\begin{array}{cc}\frac{1}{4}& 2\\ \frac{2}{3}& 4\end{array}\right|+.......$
$=4-12+2-4+1-\frac{4}{3}+.....$
$=(4+2+1+...)-(12+4+\frac{4}{3}+....)$
$=\frac{4}{1-\frac{1}{2}}-\frac{12}{1-\frac{1}{3}}$
$=8-18=-10$