JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Analyzing +4 | -1

Consider the sequence

a_1, a_2, a_3, \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

, ... 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) \ldots\left(\frac{a_{30}+\frac{1}{a_{31}}}{a_{32}}\right)

=2^\alpha\left({ }^{61} C_{31}\right)

, then

\alpha

is equal to

View answer and explanation

Correct option: C

-60

Option C (-60) is correct because after simplifying the recursive sequence and the product, the value of α can be determined.

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