To Prove:
3n ≥ 2n
Let us prove this question by principle of mathematical induction (PMI) for all natural numbers
Let P(n): 3n ≥ 2n
For n = 1 P(n) is true since 3n ≥ 2n i x e x 3 ≥ 2, which is true
Assume P(k) is true for some positive integer k , ie,
= 3k ≥ 2k....(1)
We will now prove that P(k + 1) is true whenever P( k ) is true
Consider,
[Multiplying and dividing by 2 on RHS]
Therefore, P (k + 1) is true whenever P(k) is true
By the principle of mathematical induction, P(n) is true for all natural numbers, ie, N.
Hence proved.