Let P(n) be the statement:


Let $\mathrm{P}(n)$ be the statement $: 2^{n} \geq 3 n$. If $\mathrm{P}(r)$ is true, then show that $\mathrm{P}(r+1)$ is true. Do you conclude that $\mathrm{P}(n)$ is true for all $n \in \mathbf{N}$ ?


Since, for $n=1$ i.e. P $(1)$ :

LHS $=2^{1}=2$

RHS $=3 \times 1=3$

As, LHS $<$ RHS

So, it is not true for $n=1$.

Hence, we conclude that $\mathrm{P}(n)$ is not true for all $n \in \mathbf{N}$.

Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now