2. Solved Papers
  3. JCECE Engineering

JCECE Engineering JCECE Engineering Solved Paper-2003

  • question_answer
    The sum to infinity of the series\[2+\frac{1}{2}+\frac{1}{3}+\frac{1}{{{2}^{2}}}+\frac{1}{{{3}^{2}}}+\frac{1}{{{2}^{3}}}+\frac{1}{{{3}^{3}}}+...\]

    A) \[3\]                                     

    B) \[4\]

    C) \[\frac{7}{2}\]                                   

    D)  \[\frac{9}{2}\]

    Correct Answer: C

    Solution :

    Let\[S=2+\frac{1}{2}+\frac{1}{3}+\frac{1}{{{2}^{2}}}+\frac{1}{{{3}^{2}}}+\frac{1}{{{2}^{3}}}+\frac{1}{{{3}^{3}}}+...\]                 \[=\left( 1+\frac{1}{2}+\frac{1}{{{2}^{2}}}+\frac{1}{{{3}^{2}}}+... \right)\]                 \[=\frac{1}{1-\frac{1}{2}}+\frac{1}{1-\frac{1}{3}}\]            \[(\because \]\[GP\]series)                 \[=\frac{2}{1}+\frac{3}{2}\]                 \[=\frac{7}{2}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner