Giải:
Đặt:
\(A=1+3^2+3^4+3^6+...+3^{100}\)
\(\Leftrightarrow9A=3^2+3^4+3^6+3^8+...+3^{102}\)
\(\Leftrightarrow9A-A=3^{102}-1\)
\(\Leftrightarrow8A=3^{102}-1\)
\(\Leftrightarrow A=\dfrac{3^{102}-1}{8}\)
Vậy \(A=\dfrac{3^{102}-1}{8}\).
Chúc bạn học tốt!