jee-main 2022 Q61

jee-main · India · session1_26jun_shift2 Sequences and Series Evaluation of a Finite or Infinite Sum

If $A = \sum _ { n = 1 } ^ { \infty } \frac { 1 } { \left( 3 + ( - 1 ) ^ { n } \right) ^ { n } }$ and $B = \sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { \left( 3 + ( - 1 ) ^ { n } \right) ^ { n } }$, then $\frac { A } { B }$ is equal to
(1) $\frac { 11 } { 9 }$
(2) 1
(3) $- \frac { 11 } { 9 }$
(4) $- \frac { 11 } { 3 }$

If $A = \sum _ { n = 1 } ^ { \infty } \frac { 1 } { \left( 3 + ( - 1 ) ^ { n } \right) ^ { n } }$ and $B = \sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { \left( 3 + ( - 1 ) ^ { n } \right) ^ { n } }$, then $\frac { A } { B }$ is equal to\\
(1) $\frac { 11 } { 9 }$\\
(2) 1\\
(3) $- \frac { 11 } { 9 }$\\
(4) $- \frac { 11 } { 3 }$

Paper Questions

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