Question

Consider the sequence $a_1, a_2, a_3, \ldots \ldots$ such that $a_1=1, a_2=2$ and $a_{n+2}=\frac{2}{a_{n+1}}+a_n$ for $n =1,2,3, \ldots$ If $\left(\frac{a_1+\frac{1}{a_2}}{a_3}\right) \cdot\left(\frac{a_2+\frac{1}{a_3}}{a_4}\right) \cdot\left(\frac{a_3+\frac{1}{a_4}}{a_5}\right) ... \left(\frac{a_{30}+\frac{1}{a_{31}}}{a_{32}}\right)=2^a\left({ }^{61} C_{31}\right)$, then $\alpha$ is equal to :

• A. $-30$
• B. $-31$
• C. $-60$
• D. $-61$

Answer 1

Answer: (C)

$-60$

Answer 2

The correct option is (C): -60