JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Mathematical induction and Divisibility problems

  • question_answer
    Let P (n) denote the statement that \[{{n}^{2}}+n\] is odd. It is seen that \[P(n)\Rightarrow P(n+1)\], \[{{P}_{n}}\] is true for all [IIT JEE 1996]

    A) n > 1

    B) n

    C) n > 2

    D) None of these

    Correct Answer: D

    Solution :

      \[=\sum\limits_{r=0}^{n}{{{(-1)}^{r}}{{\,}^{n}}{{C}_{r}}}.\frac{1}{{{2}^{r}}}+\sum\limits_{r=0}^{n}{{{(-1)}^{r}}}{{.}^{n}}{{C}_{r}}\frac{{{3}^{r}}}{{{2}^{2r}}}+\]. It is always odd (statement) but square of any odd number is always odd and also, sum of two odd number is always even. So for no any ?n? for which this statement is true.


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