Ta có: \(A=1+3^1+3^2+3^3+...+3^{199}+3^{200}\)
\(\Rightarrow3A=3^1+3^2+3^3+3^4+...+3^{201}\)
\(\Rightarrow3A-A=\left(3^1+3^2+3^3+3^4+...+3^{201}\right)-\left(1+3^1+3^2+3^3+...+3^{200}\right)\)
\(\Rightarrow2A=3^{201}-1\)
\(\Rightarrow A=\frac{3^{201}-1}{2}< 3^{201}-1< 3^{201}=B\)
Vậy A < B
Ta có : A = 1 + 3 + 32 + ... + 3200
\(\Leftrightarrow\)2A = 3 + 32 + 33 + ... + 3201
Lấy 2A - A = ( 3 + 32 + 33 + ... + 3201 ) - ( 1 + 3 + 32 + ... + 3200 )
\(\Rightarrow\)A = 3201 - 1
Ta thấy : 3201 - 1 < 3201
\(\Leftrightarrow\)A < B
