JEE Main & Advanced Mathematics Sequence & Series Question Bank Arithmetic Progression

  • question_answer
    The sum of the series \[\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+........\]to 9  terms is [MNR 1985]

    A)   \[-\frac{5}{6}\]

    B) \[-\frac{1}{2}\]

    C)   1

    D) \[-\frac{3}{2}\]

    Correct Answer: D

    Solution :

    Given series \[\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+........\] Here\[a=\frac{1}{2}\], common difference \[d=-\frac{1}{6}\] and \[n=9\]. \[\Rightarrow \] \[{{S}_{9}}=\frac{9}{2}\left[ 2\times \frac{1}{2}+(9-1)\left( -\frac{1}{6} \right) \right]=-\frac{3}{2}\].


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