A) \[\frac{n{{(n+1)}^{3}}}{3}\]
B) \[\frac{2n(n+1)(2n+1)}{3}\]
C) \[\frac{n(n-3)(2n+3)}{12}\]
D) \[\frac{n(n+1)(2n+4)}{6}\]
Correct Answer: B
Solution :
(b): \[S={{2}^{2}}+{{4}^{2}}+{{6}^{2}}+..........\] \[={{2}^{2}}\left[ {{1}^{2}}+{{2}^{2}}+{{3}^{2}}+.......+{{n}^{2}} \right]\] \[={{2}^{2}}\times \frac{n(n+1)\,(2n+1)}{6}\] \[=\frac{2n(n+1)(2n+1)}{3}\]You need to login to perform this action.
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