Đặt S = 2 + 2^2 + 2^3 + ... + 2^50
S=2+2^2+2^3+...+2^50
2S= 2^2+2^3+...+2^51
=>2S ‐ S = ﴾ 2^2+2^3+...+2^51 ﴿ ‐ ﴾ 2+2^2+2^3+...+2^50 ﴿
= 2^51‐2
\(\text{Đặt }A=2+2^2+2^3+...+2^{50}\)
=> \(2A=2^2+2^3+2^4+...+2^{51}\)
=> \(A=2A-A=\left(2^2+2^3+2^4+...+2^{50}\right)-\left(2+2^2+2^3+...+2^{50}\right)\)
=> \(A=2^{50}-2\)
Sửa lại xíu:
...
=> \(A=2A-A=\left(2^2+2^3+2^4+...+2^{51}\right)-\left(2+2^2+2^3+...+2^{50}\right)\)
=> \(A=2^2+2^3+2^4+...+2^{51}-2-2^2-2^3-...-2^{50}\)
=> \(A=2^{51}-2\)
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.