- #1
savtaylor2010
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Homework Statement
Prove the statement by mathematical induction:
5n + 9 < 6n for all integers n≥2
Homework Equations
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The Attempt at a Solution
Proof: let P(n) be the statement,
5n + 9 < 6n
P(2) is true because,
34<36.
Suppose that P(n) is true.
P(n+1) would be,
5n+1 + 9 < 6n+1
6n+1 = 6[itex]\bullet[/itex]6n
6[itex]\bullet[/itex](5n+9)< 6[itex]\bullet[/itex]6n
==> 54+ 6(5n) < 6[itex]\bullet[/itex]6n
==> 54+ 5(5n) + 5n < 6[itex]\bullet[/itex]6n
==> 54+ 5n+1 + 5n < 6[itex]\bullet[/itex]6n
What do I do from here? I don't know how to wrap up and prove this induction, or that P(n+1) is real? Any help would be much appreciated!
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