ISI2017-MMA-14 [closed]

Question

Let $(v_n)$ be a sequence defined by $v_1=1$ and $v_{n+1}=\sqrt{v_n^2 +(\frac{1}{5})^n}$ for $n\geq1$. Then $\lim _{n\rightarrow \infty} v_n$ is

• A. $\sqrt{5/3}$
• B. $\sqrt{5/4}$
• C. $1$
• D. nonexistent