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JEE Main & Advanced JEE Main Paper (Held on 10-4-2019 Afternoon)

  • question_answer
    The sum \[1+\frac{{{1}^{3}}+{{2}^{3}}}{1+2}+\frac{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}}{1+2+3}+....\] \[+\frac{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}+....+{{15}^{3}}}{1+2+3+....+15}-\frac{1}{2}(1+2+3+....+15)]\] [JEE Main 10-4-2019 Afternoon]

    A) 1240               

    B) 1860

    C) 660                 

    D) 620

    Correct Answer: D

    Solution :

    \[Sum=\sum\limits_{n=1}^{15}{\frac{{{1}^{3}}+{{2}^{3}}+....{{n}^{3}}}{1+2+3+....+n}-\frac{1}{2}.\frac{15.16}{2}}\]             \[=\sum\limits_{n=1}^{15}{\frac{n(n+1)}{2}}-60\]             \[=\sum\limits_{n=1}^{15}{\frac{n(n+1)(n+2-(n-1))}{6}}-60\]             \[=\frac{15.16.17}{6}-60=620\]


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