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

  • question_answer
    \[\frac{{{x}^{2}}-{{y}^{2}}}{1\,!}+\frac{{{x}^{4}}-{{y}^{4}}}{2\,!}+\frac{{{x}^{6}}-{{y}^{6}}}{3\,!}+......\infty =\]

    A) \[{{e}^{x}}-{{e}^{y}}\]

    B) \[{{e}^{{{x}^{2}}}}-{{e}^{{{y}^{2}}}}\]

    C) \[2+{{e}^{{{x}^{2}}}}-{{e}^{{{y}^{2}}}}\]

    D) \[\frac{{{e}^{x}}-{{e}^{y}}}{2}\]

    Correct Answer: B

    Solution :

    \[S=({{e}^{{{x}^{2}}}}-1)-({{e}^{{{y}^{2}}}}-1)={{e}^{{{x}^{2}}}}-{{e}^{{{y}^{2}}}}\].


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