If P(n) is the statement “2 n ≥ 3n”, and if P(r) is true, prove that P(r + 1) is true. Given. P(n) = “2 n ≥ 3n” and p(r) is true. Prove. P(r + 1) is true

Question

Philoid · Accepted Answer

we have P(n) = 2ⁿ ≥ 3n

Since, P(r) is true So,

= 2^r≥ 3r

Now, Multiply both side by 2

= 2.2^r≥ 3r.2

= 2^{r + 1}≥ 6r

= 2^{r + 1}≥ 3r + 3r [since 3r>3 = 3r + 3r≥3 + 3r]

Therefore 2^{r + 1}≥ 3(r + 1)

Hence, P(r + 1) is true.

If P(n) is the statement “2n ≥ 3n”, and if P(r) is true, prove that P(r + 1) is true.Given. P(n) = “2n ≥ 3n” and p(r) is true.Prove. P(r + 1) is true

If P(n) is the statement “2ⁿ ≥ 3n”, and if P(r) is true, prove that P(r + 1) is true.
Given. P(n) = “2ⁿ ≥ 3n” and p(r) is true.

Prove. P(r + 1) is true