Question

2²- 2³+ 2⁴- 2⁵+ ......+ 2²⁰²²+ 2²⁰²³

Answer 1

Sửa đề: \(2^2-2^3+2^4-2^5+...+2^{2022}-2^{2023}\)

Đặt \(A=2^2-2^3+2^4-2^5+...+2^{2022}-2^{2023}\)

=>\(2A=2^3-2^4+2^5-2^6+...+2^{2023}-2^{2024}\)

=>\(2A+A=2^2-2^3+2^4-2^5+...+2^{2022}-2^{2023}+2^3-2^4+...+2^{2023}-2^{2024}\)

=>\(3A=2^2-2^{2024}\)

=>\(A=\dfrac{4-2^{2024}}{3}\)

Answer 2

Sửa đề: 

`S = 2^2 - 2^3 + 2^4 - 2^5 + ... + 2^2022 - 2^2023`

`2S =  2^3 - 2^4 + 2^5 - 2^6 + ... + 2^2023 - 2^2024`

`2S + S = (2^3 - 2^4 + 2^5 - 2^6 + ... + 2^2023 - 2^2024) + ( 2^2 - 2^3 + 2^4 - 2^5 + ... + 2^2022 - 2^2023)`

`3S = 2^2 - 2^2024`

`S = ( 4 - 2^2024)/3`