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BCECE Engineering BCECE Engineering Solved Paper-2012

  • question_answer
    The coefficient of \[{{x}^{n}}\]in the series \[1+\frac{a+bx}{1!}+\frac{{{(a+bx)}^{2}}}{2!}+\frac{{{(a+bx)}^{3}}}{3!}...\infty \]

    A)  \[\frac{{{(ab)}^{n}}}{n!}\]                          

    B)         \[{{e}^{b}}.\frac{{{a}^{n}}}{n!}\]                             

    C)         \[{{e}^{a}}.\frac{{{b}^{n}}}{n!}\]                             

    D)         \[{{e}^{a+b}}\frac{{{(ab)}^{n}}}{n!}\]

    Correct Answer: C

    Solution :

    \[1+\frac{(a+bx)}{11}+\frac{{{(a+bx)}^{2}}}{2!}\] \[+\frac{{{(a+bx)}^{3}}}{3!}+...\infty ={{e}^{a+bx}}\]                 \[\therefore \]Coefficient of \[{{x}^{n}}\]                 \[{{e}^{a}}{{e}^{bx}}={{e}^{a}}.\frac{{{(b)}^{n}}}{n!}\]  


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