jee-main 2012 Q65

jee-main · India · 07may Sequences and Series Evaluation of a Finite or Infinite Sum

The sum of the series $1 ^ { 2 } + 2.2 ^ { 2 } + 3 ^ { 2 } + 2.4 ^ { 2 } + 5 ^ { 2 } + 2.6 ^ { 2 } + \ldots . + 2 ( 2 m ) ^ { 2 }$ is
(1) $m ( 2 m + 1 ) ^ { 2 }$
(2) $m ^ { 2 } ( m + 2 )$
(3) $m ^ { 2 } ( 2 m + 1 )$
(4) $m ( m + 2 ) ^ { 2 }$

The sum of the series $1 ^ { 2 } + 2.2 ^ { 2 } + 3 ^ { 2 } + 2.4 ^ { 2 } + 5 ^ { 2 } + 2.6 ^ { 2 } + \ldots . + 2 ( 2 m ) ^ { 2 }$ is\\
(1) $m ( 2 m + 1 ) ^ { 2 }$\\
(2) $m ^ { 2 } ( m + 2 )$\\
(3) $m ^ { 2 } ( 2 m + 1 )$\\
(4) $m ( m + 2 ) ^ { 2 }$

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