Question

[kevin]

Tính nhanh :

1+3²+3⁴+....+3²⁰¹⁸

Answer 1

[Shiba Inu]

Đặt A = 1 + 3² + 3⁴ +...+ 3²⁰¹⁸

\(\Rightarrow\) 3²A = 9A = 3² + 3⁴ + 3⁶ + ... + 3²⁰²⁰

\(\Rightarrow\) 9A - A = 8A = 3²⁰²⁰ - 1

\(\Rightarrow\) A = \(\dfrac{3^{2020}-1}{8}\)

Vậy 1 + 3² + 3⁴ +...+ 3²⁰¹⁸  =  \(\dfrac{3^{2020}-1}{8}\)