SOLUTION: For which positive integers n is 11n + 17 ≤ 2n? Prove the conjecture you made using mathematical induction.

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Question 923732: For which positive integers n is 11n + 17 ≤ 2n? Prove the conjecture you made using
mathematical induction.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
No positive integer n satisfies 11n + 17 <= 2n (this is equivalent to n <= -17/9).

Proof: n = 1 --> 11*1 + 17 <= 2*1, which is not true. Suppose that some k >= 1 does not satisfy inequality, which occurs iff 11k + 17 > 2k. We wish to show that k+1 also does not satisfy the inequality, i.e. we wish to show




However by hypothesis, 11k+17 > 2k, so , which is a true statement, so k+1 also does not satisfy 11n + 17 <= 2n.