JEE Main & Advanced Mathematics Sequence & Series Question Bank nth term of special series, Sum to n terms and Infinite number of terms

  • question_answer
    \[{{11}^{3}}+{{12}^{3}}+....+{{20}^{3}}\]   [Pb. CET 1997; RPET 2002]

    A) Is divisible by 5

    B) Is an odd integer divisible by 5

    C) Is an even integer which is not divisible by 5

    D) Is an odd integer which is not divisible by 5

    Correct Answer: B

    Solution :

    \[\sum\limits_{n=1}^{20}{({{n}^{3}})}-\sum\limits_{n=1}^{10}{({{n}^{3}})}=\left[ \frac{n(n+1)}{2} \right]_{n=20}^{2}-\left[ \frac{n(n+1)}{2} \right]_{n=10}^{2}\] Þ \[{{s}_{2}}={{\left[ \log \,5/3 \right]}^{2}}\] = 44100 - 3025 = 41075.


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