\(A=1+4+4^2+4^3+...+4^{99}\)
\(4A=4+4^2+4^3+4^4+...+4^{100}\)
\(3A=4^{100}-1\)
\(A=\frac{4^{100}-1}{3}\)
\(B=4^{100}\)
\(\Rightarrow\frac{B}{3}=\frac{4^{100}}{3}\)
Vì \(\frac{4^{100}-1}{3}< \frac{4^{100}}{3}\)
\(\Rightarrow A< \frac{B}{3}\)
\(\Rightarrow dpcm\)