Question

[Machi channel]

Cho A = 3+3²+3³+...+3²⁰⁰⁸.Tìm x biết : 2A+3=3^x

Answer 1

[Hoàng Thanh Huyền]

Ta có: \(A=3+3^2+3^3+...+3^{2008}\)

\(3A=3^2+3^3+3^4+...+3^{2009}\)

\(3A-A=3^{2009}-3\)

Hay \(2A=3^{2009}-3\)

\(\Rightarrow2A+3=3^x\)

\(\Rightarrow\left(3^{2009}-3\right)+3=3^x\)

\(\Rightarrow3^{2009}=3^x\)

\(\Rightarrow x=2009\)

Hok tốt nha^^

Answer 2

[‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍...]

Có A=3+3²+...+3²⁰⁰⁸

=>3A=3²+3³+...+3²⁰⁰⁹

=>3A-A=2A=3²⁰⁰⁹-3

Thay 2A vào 2A+3=3^x

Ta được: 3²⁰⁰⁹-3+3=3^x

=>3²⁰⁰⁹=3^x

=>x=2009

Vậy..