JEE Main 202226 Jun, Evening shiftMathematicsMediumSequence and Series179× since 2002If A=∑n=1∞1(3+(−1)n)nA = \sum\limits_{n = 1}^\infty {{1 \over {{{\left( {3 + {{( - 1)}^n}} \right)}^n}}}}A=n=1∑∞(3+(−1)n)n1 and B=∑n=1∞(−1)n(3+(−1)n)nB = \sum\limits_{n = 1}^\infty {{{{{( - 1)}^n}} \over {{{\left( {3 + {{( - 1)}^n}} \right)}^n}}}}B=n=1∑∞(3+(−1)n)n(−1)n, then AB{A \over B}BA is equal to :AOption A. 119{{11} \over 9}911BOption B. 1COption C. −-−119{{11} \over 9}911DOption D. −-−113{{11} \over 3}311CheckSkip · show solution
