gọi tổng là A.ta có
\(A=1+2+2^2+....+2^{10}\)
\(\Rightarrow2A=2+2^2+2^3+...+2^{11}\)
\(\Rightarrow2A-A=\left(2+2^2+2^3+...+2^{11}\right)-\left(1+2+2^2+....+2^{10}\right)\)
\(\Rightarrow A=2^{11}-1\)
A=1+2+22+...+210
=>2A=2+22+23+...+211
=>2A-A=(2+22+23+...+211)-(1+2+22+...+210)=211-1