Đặt \(A=2+2^2+2^3+...+2^{50}\), ta có:
\(A=2+2^2+2^3+...+2^{50}\)
\(\Rightarrow2A=2\left(2+2^2+2^3+...+2^{50}\right)\)
\(\Rightarrow2A=4+2^3+2^4+...+2^{51}\)
\(\Rightarrow A=2A-A=\left(4+2^3+2^4+...+2^{51}\right)-\left(2+2^2+2^3+...+2^{50}\right)\)
\(\Rightarrow A=4+2^3+2^4+...+2^{51}-2-2^2-2^3-...-2^{50}\)
\(\Rightarrow A=2^{51}-2\)
Chúc bạn học tốt.