jee-main 2012 Q65

jee-main · India · 26may Sequences and Series Evaluation of a Finite or Infinite Sum
If the sum of the series $1 ^ { 2 } + 2 \cdot 2 ^ { 2 } + 3 ^ { 2 } + 2 \cdot 4 ^ { 2 } + 5 ^ { 2 } + \ldots 2.6 ^ { 2 } + \ldots$ upto n terms, when n is even, is $\frac { n ( n + 1 ) ^ { 2 } } { 2 }$, then the sum of the series, when n is odd, is
(1) $n ^ { 2 } ( n + 1 )$
(2) $\frac { n ^ { 2 } ( n - 1 ) } { 2 }$
(3) $\frac { n ^ { 2 } ( n + 1 ) } { 2 }$
(4) $n ^ { 2 } ( n - 1 )$
If the sum of the series $1 ^ { 2 } + 2 \cdot 2 ^ { 2 } + 3 ^ { 2 } + 2 \cdot 4 ^ { 2 } + 5 ^ { 2 } + \ldots 2.6 ^ { 2 } + \ldots$ upto n terms, when n is even, is $\frac { n ( n + 1 ) ^ { 2 } } { 2 }$, then the sum of the series, when n is odd, is\\
(1) $n ^ { 2 } ( n + 1 )$\\
(2) $\frac { n ^ { 2 } ( n - 1 ) } { 2 }$\\
(3) $\frac { n ^ { 2 } ( n + 1 ) } { 2 }$\\
(4) $n ^ { 2 } ( n - 1 )$