- #1
leo255
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Homework Statement
Prove by mathematical induction: 2^n >= 11n + 17, for n >= 7, and n is an integer.
Homework Equations
The Attempt at a Solution
This is my attempt - I want to see if I'm doing this correctly.
2^n >= 11n + 17, n >= 7
basis 2^7 >= 77 + 17
128 >= 94. True.
Induction Hypothesis:
Assume true:
2^k >= 11k + 17
Must prove:
2^k+1 >= 11(k+1) + 17
2^k * 2 >= 2*(11k + 17) <-- By induction hypothesis, just multiplying both sides by 2.
2^k * 2 >= 22k + 34
2^k*2 >= 11(k + 1) + 17
2^k*2 >= 11k + 28
2^k+1 >= 11k+28, because
2^k+1 >= 22k + 34, and 11k + 28 will always be a smaller number.