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JEE Main & Advanced JEE Main Paper (Held on 7 May 2012)

  • question_answer
    The sum of the series\[{{\text{1}}^{\text{2}}}+\text{2}.{{\text{2}}^{\text{2}}}+{{\text{3}}^{\text{2}}}+\text{2}.{{\text{4}}^{\text{2}}}+{{\text{5}}^{\text{2}}}+\text{2}.{{\text{6}}^{\text{2}}}+....+\text{2(2m}{{\text{)}}^{\text{2}}}\]is   JEE Main Online Paper (Held On 07 May 2012)

    A) \[m{{(2m+1)}^{2}}\]                      

    B)                        \[{{m}^{2}}(m+2)\]

    C)                        \[{{m}^{2}}(2m+1)\]                      

    D)                        \[m{{(m+2)}^{2}}\]

    Correct Answer: A

    Solution :

                    The sum of the given series \[{{1}^{2}}+{{2.2}^{2}}+{{3}^{2}}+{{2.4}^{2}}+{{5}^{2}}+{{2.6}^{2}}+\]??\[+2{{(2m)}^{2}}\]is \[\frac{2m{{(2m+1)}^{2}}}{2}=m{{\left( 2m+1 \right)}^{2}}\]


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