proof

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April 30th 2012, 08:02 AM
Mhmh96

proof

How to prove that:

1994^2000+1995^2000<1996^2000
April 30th 2012, 08:24 AM
emakarov

Re: proof

$1996^{2000}=(1995+1)^{2000}=1995^{2000}+2000\cdot1 995^{1999}+\dots$ . Now, $2000\cdot1995^{1999}>1994\cdot1994^{1999}=1994^{20 00}$ .

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