How to prove that: 1994^2000+1995^2000<1996^2000
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$\displaystyle 1996^{2000}=(1995+1)^{2000}=1995^{2000}+2000\cdot1 995^{1999}+\dots$. Now, $\displaystyle 2000\cdot1995^{1999}>1994\cdot1994^{1999}=1994^{20 00}$.
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