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Oct 29th, 2002, 07:37 AM
#1
[RESOLVED] I need to prove something.
This is a school assignment, so all the people that don't like to help at such problems are warned.
I have to use complete deduction to prove that
3n + 2^n < 3^n
is true for every n >= 3.
I can prove that it is true for n0 = 3 (surprise), then I tried to prove that the difference:
(3ni + 2^ni) - (3ni-1 + 2^ni-1) < (3^ni) - (3^ni-1)
I end up with
18 + (3*2^ni) < 4*3^ni
but I can't get the n down from the powers. I can't use logarithm because of the addition.
Anyone knows how to solve this, or knows a completly different better solution? It has to use deduction though.
Last edited by CornedBee; Nov 4th, 2002 at 05:13 AM.
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 CornedBee
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