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JEE Main & Advanced Mathematics Sequence & Series Question Bank Exponential series

  • question_answer
    \[\frac{1}{2}+\frac{1}{4}+\frac{1}{8(2)\,!}+\frac{1}{16\,(3)\,!}+\frac{1}{32(4)\,!}+......\infty =\]

    A) \[e\]

    B) \[\sqrt{e}\]

    C) \[\frac{\sqrt{e}}{2}\]

    D) None of these

    Correct Answer: C

    Solution :

    \[S=\frac{1}{2}\left\{ 1+\frac{\left( \frac{1}{2} \right)}{1!}+\frac{{{\left( \frac{1}{2} \right)}^{n}}}{2!}+.... \right\}=\frac{1}{2}{{e}^{1/2}}=\frac{\sqrt{e}}{2}\].


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