So sánh 2^30 + 3^30 + 4^30

Ta có:

\({4^{30}} = {2^{30}} \cdot {2^{30}} = {\left( {{2^3}} \right)^{10}} \cdot {\left( {{2^2}} \right)^{15}} > {8^{10}} \cdot {3^{15}} > \left( {{8^{10}} \cdot {3^{10}}} \right) \cdot 3 = {24^{10}} \cdot 3\)

Vậy \({2^{30}} + {3^{30}} + {4^{30}} > 3 \cdot {24^{10}}.\)