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vikkisut88
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Homework Statement
Prove that ([tex]\forall[/tex]n in the set of Natural numbers )[(n [tex]\geq[/tex] 9) [tex]\Rightarrow[/tex] (2n > 4n2 + 1)]
Homework Equations
To do proof by induction you must first prove for n = 1, then assume true for n and then show for n+1
The Attempt at a Solution
So for n=1 i have RHS:29 = 512 and 4.92 + 1 = 325
So (2n > 4n2 + 1)] for n=1
Now assume true for n
Show for n+1: (2n+1 > 4(n+1)2 + 1)]
So 2 n+1can also be written as 2 n . 21
Thus 2 n+1> 4(n+1) 2 + 1)] = 2n . 21 > [4(n+1)2 + 1].2
which is the same as 2n . 21 > 8(n+1)2 + 2
And now I'm stuck as to how to arrange this to give me the right answer
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