Question

1.1+2+2\(^2\)+2\(^3\)+.............+2\(^{10}\)

Answer 1

Đặt :

\(A=1+2+2^2+2^3+...............+2^{10}\)

\(\Leftrightarrow2A=2+2^2+2^3+..............+2^{11}\)

\(\Leftrightarrow2A-A=\left(2+2^2+2^3+.......+2^{11}\right)-\left(1+2+2^2+......+2^{10}\right)\)

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

Answer 2

Đặt \(A=1+2+2^2+2^3+...+2^{10}\)

\(\Leftrightarrow2A=2+2^2+2^3+2^4+...+2^{11}\)

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

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