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10th Class Mathematics Real Numbers Question Bank Real Number

  • question_answer
    Find the sum of \[{{\mathbf{2}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{4}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{6}}^{\mathbf{2}}}........{{\mathbf{(2n)}}^{\mathbf{2}}}\].

    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): \[S={{2}^{2}}+{{4}^{2}}+{{6}^{2}}+..........\] \[={{2}^{2}}\left[ {{1}^{2}}+{{2}^{2}}+{{3}^{2}}+.......+{{n}^{2}} \right]\] \[={{2}^{2}}\times \frac{n(n+1)\,(2n+1)}{6}\] \[=\frac{2n(n+1)(2n+1)}{3}\]


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