2. Solved Papers
  3. Manipal Engineering

Manipal Engineering Manipal Engineering Solved Paper-2013

  • question_answer
    The least positive integer\[n\], for which\[n!<{{\left( \frac{n+1}{2} \right)}^{n}}\], is

    A)  1                                            

    B)  2            

    C)  3                            

    D)         4

    Correct Answer: B

    Solution :

    For\[n=1\],         \[1!<{{(1)}^{1}}\] that is,\[1<1\]is not true. For\[n=2\],         \[2!<{{\left( \frac{3}{2} \right)}^{1}}\] that is,\[2<\frac{9}{4}\]is true, By induction,\[n!<{{\left( \frac{n+1}{2} \right)}^{n}}\forall n\in N\]for\[n>2\] \[\therefore \]least\[n=2\].


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