Using mathematical induction, I need to show 4^n is greater than or equal to 4n for all positive integers.  I'm stuck on the last step, where I need to show 4^k+1 is greater than or equal to 4k+1.

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Nathan -For n=1: 4^1 ≥ 4(1)  THIS IS TRUEFor n=k: 4^k ≥ 4(k)  ASSUMED TO BE TRUEShow for n=k+1: 4^(k+1) ≥ 4(K+1) = 4K + 4Start with the statement that is assumed true:4^k ≥ 4(k)4[4^k] ≥ 4[4(k)] : Multiply both sides by 44^(k+1) ≥ 4[4(k)]Now, focus on the right side of the inequality:4[4(k)] = 4k + 4k + 4k +4k4k + 4k + 4k +4k ≥ 4k + 4 + 4 + 4 for all k>14k + 4 + 4 + 4 > 4k + 4 = 4(k+1) so it follows:4^(k+1) ≥ 4[4(k)] ≥ 4(k+1) for all integers k≥1Hope that helps