Question

Tính \(S=1+2+2^2+...+2^{10}\)

Answer 1

ta có : \(2S=2\left(1+2+2^2+...+2^{10}\right)=2+2^2+2^3+...+2^{11}\)

\(\Rightarrow2S-S=2+2^2+2^3+...+2^{11}-\left(1+2+2^2+...+2^{10}\right)\)

\(\Leftrightarrow S=2^{11}-1\)

Answer 2

Ta có:\(S=1+2+2^2+...+2^{10}\)

\(\Rightarrow2.S=2+2^2+2^4+...+2^{11}\)

\(\Rightarrow2.S-S=\left(2+2^2+2^4+...+2^{11}\right)-\left(1+2+2^2+...+2^{10}\right)\)

\(\Rightarrow S=2^{11}-1\)

Chúc bạn học tốt!!!