JEE Advance - Mathematics (1988 - No. 17)
The sum of the first n terms of the series $${1^2} + {2.2^2} + {3^2} + {2.4^2} + {5^2} + {2.6^2} + .........$$ is
$$n\,\,{\left( {n + 1} \right)^2}/2,$$ when $$n$$ is even. When $$n$$ is odd, the sum is .............
$$n\,\,{\left( {n + 1} \right)^2}/2,$$ when $$n$$ is even. When $$n$$ is odd, the sum is .............
$${{{n^2}left( {n + 1}
ight)} \over 4}$$
$${{{n^2}left( {n + 1}
ight)} \over 2}$$
$${{{nleft( {n + 1}
ight)} \over 2}}$$
$${{{n^2}left( {n + 1}
ight)^2} \over 2}$$
$${{{nleft( {n + 1}
ight)^2} \over 2}$$