Question

A=1-2-2^3-2^3+2^4-...+2^2022B=1+3+3^2+3^3+3^4+...+3^2022

Answer 1

A= 1 - 2 - 2² - 2³ + 2⁴ +...+ 2²⁰²² (sửa đề)

 = -13 + (2⁴ + 2⁵ + 2⁶ + ... + 2²⁰²²)

2A = -26 + (2⁵ + 2⁶ + 2⁷ +  ... + 2²⁰²³)

2A - A = -26 + (2⁵ + 2⁶ + 2⁷ +  ... + 2²⁰²³) -  [-13 + (2⁴ + 2⁵ + 2⁶ + ... + 2²⁰²²)]

A = -13 +(2²⁰²³ - 2⁴)

= 2²⁰²³ - 29

Vậy...

B = 1 + 3 + 3² + 3³ + 3⁴ + ... + 3²⁰²²

3B = 3 + 3² + 3³ + 3⁴ + 3⁵ +...+ 3²⁰²³

3B - B = 3 + 3² + 3³ + 3⁴ + 3⁵ +...+ 3²⁰²³ - (1 + 3 + 3² + 3³ + 3⁴ + ... + 3²⁰²²)

2B = 3²⁰²³ - 1

=> B = \(\dfrac{3^{2023}-1}{2}\)

Vậy...

#Ayumu