Question

tính tổng : 1+2+2²+2³+...+2¹⁰

Answer 1

gọi tổng là A.ta có

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

\(\Rightarrow2A=2+2^2+2^3+...+2^{11}\)

\(\Rightarrow2A-A=\left(2+2^2+2^3+...+2^{11}\right)-\left(1+2+2^2+....+2^{10}\right)\)

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

Answer 2

A=1+2+2²+...+2¹⁰

=>2A=2+2²+2³+...+2¹¹

=>2A-A=(2+2²+2³+...+2¹¹)-(1+2+2²+...+2¹⁰)=2¹¹-1