Question

Cho A = 5+5^2+5^3+...+5^2016

Tìm n để 4A+5=5^n-1

Giải giùm mk nha 

Answer 1

A=5+5²+...+5²⁰¹⁶

5A=5²+5³+...+5²⁰¹⁷

5A-A=(5²+5³+...+5²⁰¹⁷)-(5+5²+...+5²⁰¹⁶)

4A = 5²⁰¹⁷ - 5

=> 4A + 5 = 5²⁰¹⁷ - 5 + 5 = 5²⁰¹⁷ = 5^n-1

=> n-1=2017 => n=2018

Answer 2

A = 5 + 5² + 5³ + ............ + 5²⁰¹⁶

5A = 5² + 5³ + 5⁴ + .............. + 5²⁰¹⁷

5A - A = ( 5² + 5³ + 5⁴ + ................ + 5²⁰¹⁷ ) - ( 5 + 5² + 5³ + ................. + 5²⁰¹⁶ )

5A - A = 5² + 5³ + 5⁴ + ........... + 5²⁰¹⁷ - 5 - 5² - 5³ - .............. - 5²⁰¹⁶

4A = 5²⁰¹⁷ - 5

4A + 5 = 5^n-1

\(\Rightarrow\) 4A + 5 = 5²⁰¹⁷ - 5 + 5 = 5²⁰¹⁷ = 5^n-1

\(\Rightarrow\) n - 1 = 2017 

\(\Rightarrow\) n = 2018

Vậy n = 2018

Answer 3

A=5.5^2+...+5^2016

5A=5^2+5^3+...+2017

5A-A=(5^2+5^3+...+5^2017)-(5+5^2+5^3+...+5^2016)

4A=5^2017-5

=>4A+5=5^2017-5+5 =5^2017=5^n-1

=>n-1=2017=>n=2018

mk ko biết đúng hay sai nhé