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$The sum of the first n terms of the series 1^{2} + {2.2}^{2} + 3^{2} + {2.4}^{2} + 5^{2} + .$ $Is \frac{n (n + 1)^{2}}{2}, when n is even, when 'n' is odd sum is$

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n(n+1)22

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detailed solution

Correct option is B

If n is odd, the required sum is 12+2.22+32+2⋅42+52+..+2(n−1)2+n2=(n−1)n22+n2=n2(n+1)2

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The sum of the first n terms of the series 12+2.22+32+2.42+52+. Is n(n+1)22, when n is even, when 'n' is odd sum is

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$The sum of the first n terms of the series 1^{2} + {2.2}^{2} + 3^{2} + {2.4}^{2} + 5^{2} + .$ $Is \frac{n (n + 1)^{2}}{2}, when n is even, when 'n' is odd sum is$