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

Open in App

Solution

$Since, for n = 1 i . e . P (1) : LHS = 2^{1} = 2 RHS = 3 \times 1 = 3 As, LHS < RHS So, it is not true for n = 1 . Hence, we conclude that P (n) is not true for all n \in N .$

Suggest Corrections

Similar questions

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

If P (n) is the statement "2" $\leq$ "3n", and If P (r) is true, prove that P (r + 1) is true.

P (n)

" 3^{n} > n "

P (n)

P (n + 1)

If P(n) is the statement "n^2 + n is even", and if P (r) is true, then P (r + 1) is true.