Question

 

Giup mk voi

Answer 1

\(A=3+3^2+3^3+3^4+...+3^{100}\)

\(3A=3^2+3^3+3^4+3^5+...+3^{101}\)

\(3A-A=3^{101}-1\)

\(2A=3^{101}-1\)

\(A=\frac{3^{101}-1}{2}\)

Vì \(\frac{3^{101}-1}{2}< 3^{101}-1\)

\(\Rightarrow A< B\)

\(\Rightarrow dpcm\)

Answer 2

\(A=1+4+4^2+4^3+...+4^{99}\)

\(4A=4+4^2+4^3+4^4+...+4^{100}\)

\(3A=4^{100}-1\)

\(A=\frac{4^{100}-1}{3}\)

\(B=4^{100}\)

\(\Rightarrow\frac{B}{3}=\frac{4^{100}}{3}\)

Vì \(\frac{4^{100}-1}{3}< \frac{4^{100}}{3}\)

\(\Rightarrow A< \frac{B}{3}\)

\(\Rightarrow dpcm\)