Sequences And Series

ধরি একটি শ্রেণি \({a_1},{a_2},{a_3},\,...\) যেখানে \({a_1} = 1,{a_2} = 2\) এবং \({a_{n + 2}} = {2 \over {{a_{n + 1}}}} + {a_n}\), সকল \(n = 1,2,3,\,...\) । যদি \(\left( {{{{a_1} + {1 \over {{a_2}}}} \over {{a_3}}}} \right).\left( {{{{a_2} + {1 \over {{a_3}}}} \over {{a_4}}}} \right).\left( {{{{a_3} + {1 \over {{a_4}}}} \over {{a_5}}}} \right)....\left( {{{{a_{30}} + {1 \over {{a_{31}}}}} \over {{a_{32}}}}} \right) = {2^\alpha }\left( {{}^{61}{C_{31}}} \right)\), তবে \(\alpha\) এর মান হবে ঃ