JEE Main & Advanced Sample Paper JEE Main - Mock Test - 6

  • question_answer
    If m is a natural number, then

    A) \[{{1}^{2}}+{{2}^{2}}+.....+{{n}^{2}}<{{n}^{3}}/3\]

    B) \[{{1}^{2}}+{{2}^{2}}+.....+{{n}^{2}}={{n}^{3}}/3\]

    C) \[{{1}^{2}}+{{2}^{2}}+.....+{{n}^{2}}>{{n}^{3}}\]

    D) \[{{1}^{2}}+{{2}^{2}}+.....+{{n}^{2}}>{{n}^{3}}/3\]

    Correct Answer: D

    Solution :

    [d]:\[{{1}^{2}}+{{2}^{2}}+...+{{n}^{2}}=\frac{n(n+1)(2n+1)}{6}\] \[=\frac{n\times (n+1)(n+1/2)}{3}>\frac{n.n.n}{3}=\frac{{{n}^{3}}}{3}\] [\[\because \]\[n+1>n\]and \[n+1/2>n\]]


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