If P(n) is the statement “2n ≥ 3n”, and if P(r) is true, prove t – InterviewSolution

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1.

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

Answer»

Given.

P(n) = “2ⁿ ≥ 3n” and p(r) is true.

Prove. P(r + 1) is true

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

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