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

  • question_answer
    In  the expansion of  \[\frac{{{e}^{5x}}+{{e}^{x}}}{{{e}^{3x}}}\], the coefficient of  \[{{x}^{4}}\]is

    A) - \[6/5\]

    B) 4/3

    C) - 4/3

    D) None of these

    Correct Answer: B

    Solution :

    \[\frac{{{e}^{5x}}+{{e}^{x}}}{{{e}^{3x}}}={{e}^{2x}}+{{e}^{-2x}}=2\left\{ 1+\frac{{{(2x)}^{2}}}{2\ !}+\frac{{{(2x)}^{4}}}{4\ !}+...... \right\}\] Coefficient of\[{{x}^{4}}=2.\frac{{{2}^{4}}}{4\ !}=\frac{4}{3}\].


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