jee-main 2021 Q62

jee-main · India · session1_24feb_shift2 Sequences and Series Evaluation of a Finite or Infinite Sum
If $n \geqslant 2$ is a positive integer, then the sum of the series ${ } ^ { n + 1 } C _ { 2 } + 2 \left( { } ^ { 2 } C _ { 2 } + { } ^ { 3 } C _ { 2 } + { } ^ { 4 } C _ { 2 } + \ldots + { } ^ { n } C _ { 2 } \right)$ is
(1) $\frac { n ( n - 1 ) ( 2 n + 1 ) } { 6 }$
(2) $\frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 }$
(3) $\frac { n ( n + 1 ) ^ { 2 } ( n + 2 ) } { 12 }$
(4) $\frac { n ( 2 n + 1 ) ( 3 n + 1 ) } { 6 }$ 
If $n \geqslant 2$ is a positive integer, then the sum of the series ${ } ^ { n + 1 } C _ { 2 } + 2 \left( { } ^ { 2 } C _ { 2 } + { } ^ { 3 } C _ { 2 } + { } ^ { 4 } C _ { 2 } + \ldots + { } ^ { n } C _ { 2 } \right)$ is\\
(1) $\frac { n ( n - 1 ) ( 2 n + 1 ) } { 6 }$\\
(2) $\frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 }$\\
(3) $\frac { n ( n + 1 ) ^ { 2 } ( n + 2 ) } { 12 }$\\
(4) $\frac { n ( 2 n + 1 ) ( 3 n + 1 ) } { 6 }$
Paper Questions
Q61 Q62 Q63 Q64 Q65 Q66 Q67