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clic-clac · #2 November 16th, 2008, 11:57 AM

Have you checked that $3^{3^{3}}>79.(3^{3})^{2}$ ?

Then, let $n \geq 3^{3}$ be an integer, and assume that $3^{n}>79n^{2}$ (induction hypothesis)

$79(n+1)^{2}=79n^{2}+79(2n)+79$

Is it true that, if $n\geq 3^{3}\$ , then $\ 2n\leq n^{2}$ and $1\leq n^{2}$ ?

If it's the case, $79n^{2}+79(2n)+79 \leq 79n^{2}+79n^{2}+79n^{2}=3(79n^{2})$

What can we conclude using the induction hypothesis?

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