Question

Cho A = 3+3²+3³+...+3²⁰⁰⁹

Tìm số tự nhiên n biết rằng 2A+3=3ⁿ

Answer 1

3A=3^2+3^3+3^4+...+3^2010

2A=3^2010-3

2A+3=3^2010-3+3=3^n

3^2010=3^n

n=2010

Answer 2

A=3+3^2+3^3+...+3^2009

=>3A=3^2+3^3+3^4+...+3^2010

=>3A-A=3^2010-3

=>2A=3^2010-3

=>2A+3=3^2010

=>n=2010

Answer 3

3A = 3( 3+3²+3³+ ... +3²⁰⁰⁹)

3A = 3²+3³+ ... +3²⁰¹⁰

3A - A = ( 3²+3³+ ... +3²⁰¹⁰) - ( 3+3²+3³+ ... +3²⁰⁰⁹⁾

2A = 3²⁰¹⁰ - 3

Ta có 2A+3=3ⁿ

=> 3²⁰¹⁰ - 3 + 3 = 3ⁿ

3²⁰¹⁰ = 3ⁿ  => n=2010