Question

thu gọn tổng: A= 2+2^2+2^3+...+2^159+2^160

 

 

Answer 1

A=2+2²+2³+...+2¹⁶⁰

2A=2²+2³+...+2¹⁶¹

2A-A=(2²+2³+...+2¹⁶¹)-(2+2²+2³+...+2¹⁶⁰)

A=2¹⁶¹-2

Answer 2

Ta có \(2A=2^2+2^3+2^4+...+2^{161}\Rightarrow2A-A=\left(2^2+2^3+...+2^{161}\right)-\left(2+2^2+...+2^{160}\right)\Rightarrow A=2^{161}-2\)

Answer 3

Ta có: \(A=2+2^2+2^3+...+2^{159}+2^{160}\)

\(\Leftrightarrow2\cdot A=2^2+2^3+2^4+...+2^{160}+2^{161}\)

\(\Leftrightarrow2A-A=2^2+2^3+2^4+...+2^{160}+2^{161}-2-2^2-2^3-...-2^{159}-2^{160}\)

\(\Leftrightarrow A=2^{161}-2\)