Question

Tính nhanh:

1+2+2^2+2^3+...+2^62+2^63+2^64

giúp mình nhé cảm  ơn

Answer 1

Đặt \(A=1+2+2^2+2^3+...+2^{64}\)

\(\Rightarrow2A=2+2^2+2^3+...+2^{65}\)

\(\Rightarrow2A-A=2+2^2+2^3+...+2^{65}-\left(1+2+2^2+...+2^{64}\right)\)

\(\Rightarrow A=2+2^2+2^3+...+2^{65}-1-2-2^2-...-2^{64}\)

\(\Rightarrow A=2^{65}-1\)