> This is for the information to all those candidates who have registered and paid the fees for the KVPY Aptitude test-2021. The KVPY Aptitude test will now be held on 9th January 2022
in his day, from all I hear, and he started my collection. Itβs a nice collection too, blocks of four of practically every U.S. issue, first-day covers, and so on. President Roosevelt collected stamps too, you know.
Let $\overrightarrow{\mathbf{v}}_{0}$ be a fixed vector and $\overrightarrow{\mathbf{v}}_{0}=\left[\begin{array}{l}1 \\ 0\end{array}\right]$. Then for $n \geq 0$ a sequence is defined $\overrightarrow{\mathbf{v}}_{n+1}=\overrightarrow{\mathbf{v}}_{n}+\left(\frac{1}{2}\right)^{n+1}\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]^{n+1} \overrightarrow{\mathbf{v}}_{0}$ then $\lim _{n \rightarrow \infty} \overrightarrow{\mathbf{v}}_{n}=\left[\begin{array}{l}\alpha \\ \beta\end{array}\right]$. Find $\frac{\alpha}{\beta}$
