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JEE Advanced Mathematics question

MathematicsSequence and SeriesJEE Advanced

If \displaystyle\sum_{k=1}^{n}\left(\sum_{m=1}^{k}m^{2}\right)=an^{4}+bn^{3}+cn^{2}+dn+e then

Answer: (A),(C),(D)

Solution

Missing argument for \frac\frac{k(k+1)(2k+1)}6=Missing argument for \frac\frac16++k)=Missing argument for \frac\frac13{Missing argument for \frac\frac{n(n+1)}2}^2+Missing argument for \frac\frac12·Missing argument for \frac\frac{n(n+1)(2n+1)}6+Missing argument for \frac\frac16·Missing argument for \frac\frac{n(n+1)}2.

Simplifying, this equals . Since the identity holds for all ,

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Question ID VK-107878