Dễ thấy:64^{12}=\left(4^3\right)^{12}=4^{3.12}=4^{36}6412=(43)12=43.12=436
Ta có: 4S=4\left(4^0+4^1+4^2+4^3+...+4^{35}\right)4(40+41+42+43+...+435)
=4^1+4^2+4^3+4^4+...+4^{36}=41+42+43+44+...+436
=>4S-S=4^{36}-4^0436−40
Hay 3S=4^{36}-1< 4^{36}=64^{12}436−1<436=6412
Vậy 3S<64^{12}6412