if p (n)is the statement "2n is greater than or equal to 3n" and if pr is true prove that - Maths - Principle of Mathematical Induction

Question

if p (n)is the statement "2n is greater than or equal
to 3n" and if pr is true prove that p(r+1) is true

Ankush Jain · Accepted Answer

Given, p(n) be the statement stated as : p(n) = 2n â‰¥ 3n Again, it is given that p(r) is true $\Rightarrow p (r) = 2^{r} \geq 3 r \Rightarrow 2 \cdot 2^{r} \geq 2 \cdot 3 r \Rightarrow 2^{r + 1} \geq 6 r \Rightarrow 2^{r + 1} \geq 3 r + 3 r$ $\Rightarrow 2^{r + 1} \geq 3 r + 3 [\begin{matrix} ∵ 3 r \geq 3 \\ \Rightarrow 3 r + 3 r = 3 + 3 r \end{matrix}]$ $\Rightarrow 2^{r + 1} \geq 3 (r + 1) \Rightarrow p (r + 1) is true$

if p (n)is the statement "2n is greater than or equal to 3n" and if pr is true prove that p(r+1) is true.

if p (n)is the statement "2ⁿ is greater than or equal to 3n" and if pr is true prove that p(r+1) is true.